Good afternoon Giorgi,

REMEMBER: Just as we have probably all heard so brilliantly in the movie "Pirates of the Caribbean" - the code is more like guidelines than actual rules. - Something to keep in mind when intentionally diving head first down the rabbit hole of understanding the science of English. Of course there are prescribed writing methods and standards, and if you are subject to any of them, you would do well to not falter. But, enough preface.
ULTIMATELY: You have misunderstood the premise in the rule, or guideline, to a certain extent. In the spherical example, it is not discussing a single sphere, but the separate economic, social, and cultural spheres. In the dressed example, it is not discussing a single dress, but both black and also white ones. But of course, you knew that from each case, based upon what was written - therefore, the author conveyed the/his meaning effectively, and it was not left in question.
Both of these examples are the same, and have adequately used the articles such that you understand the meaning. Ultimately, that is the only real point of the rules and guidelines with which to write; they are meant to curb misunderstanding(s).
HOWEVER: The rule that you have described is in fact incomplete. The use of articles is meant to properly assign the describing modifier(s) to the appropriate noun (or otherwise item) in order to convey the meaning.
Should the thought ever occur to you that if you simply write: "red and white roses" - someone will believe that you have roses bespeckled with hues of red and white in a pinkish firework display of botanical delight - then you might want to use the definite article in front of both of the adjectives/modifiers. Example: "The red and the white roses were neat." Thus, you have clearly conveyed to any reader that the roses you were referencing were of the red variety and also of the white variety, exclusively.
THE POINT: In the case of the different "spheres" - You clearly understood that the spheres were at least somewhat autonomous, and that you were not meant to see the political, social, and cultural sphere as one and the same, but three separate spheres. Had you seen the different "political" "social" and "cultural" spheres as the same sphere, then you very likely would have been distracted, even if only for a brief moment in time, from what the author was ACTUALLY trying to discuss, which was the so-called "reforms" discussed in the subject of this sentence. Therefore, the meaning was conveyed adequately, and the author was able "to get on with" discussing the reforms, or their implementation(s) in the aforementioned spheres, and so on and so forth.
IN my HUMBLE opinion: It is not MORE correct to have the definite article, in general. BUT: There does exist this rule where if the subject/item/object or subjects/items/objects being discussed are separate, and you reference them in a list form, that you should use the definite article for each modifier, in order to clearly convey the separation.
FURTHERMORE: You may find that it also depends on the usage in the sentence. Is it being used in the subject, predicate, subordinate clauses, etc.? Or more importantly, it also depends (as I have somewhat belaboured above) on what the focus of the sentence, discourse, or content needs to be. You might say:
"The economic, social, and cultural spheres wherein the principles of American capitalism need considerable reformation are not too abstract for us to implement real, effective strategy, in order that all parties involved would ultimately reap the benefit."
And you might just as quickly need to say:
"The economic, the social, and the cultural spheres must be viewed without our own individual prejudices and opinions taking precedence over our full comprehension of their seemingly impossible complexities, in order to see that they are simply not as autonomous as many politicians would lead us to believe."
Did you catch the meaningful emphasis used (quite well I might add, though I say so myself) in each example?

Also, don't get me started on the indefinite article, as it does carry much of the same guideline - but it has very different implementation.

Very best regards,
Wordsmithy

Forgive me, I should add that "lastronin" [of whose ceased indentured servitude's validity I question... :P ;-) ] has also made a very helpful and description; however, I question the use of "correspondences" as referencing plural letters over one or more exchanges, just as he put so well: "Just say 'letters'," and get on with it.
I questions this BECAUSE there IS a REASON you should just say letters: The letters are the letters, and the act of corresponding is not directly relevant to the number of letters. It isn't necessarily wrong, with this I agree whole-heartedly; however, it is usually USED incorrectly, and therefore: "A WITCH"

Thank you, lastronin for encouraging us to "get on with it."

ULTIMATELY: Please read in its entirety the entry by xavier_onassis, whose example is so far the best. Based upon the original question, xavier has provided several examples that effectively communicate the usage of the word correspondence with or without its plural form, in both the non-countable sense, and a clearly defined plural noun form. It is not impossible to have a plural of the word correspondence, unless you are referring to letters, mail, etc., and not to the "noun" form of the "verb" to correspond, which obviously has a plural form, if you are referring to multiple cases of somethings or someones corresponding to any number of somethings or someones. (Please indulge me in my use of something and someone in pluralities, as they seem to befit the current topic, although also adding to the general pandemonious chatter)

(Please also indulge me in my use of "pluralities" - as it seems the most fitting word, but, again, it does seem to invoke a sort of ironic havoc upon our discussion)

HOWEVER: Let us take a step back and remind ourselves of both the original question and the majority usage of the word correspondence:

"The House of Parliament acknowledges receipt of correspondence dated July 4, 1776, wherein it is requested that the Sovereignty of the British Commonwealth respond to the previously addressed concerns of mistreatments, misrepresentations, oppressions and general malfeasance, by recognizing the newly-founding peoples in the British-occupied regions of North America, specifically along the North-Eastern portions North of Mexico and South of Canada, as a free and independent Republic, under its own bona fide Sovereignty."

Even if the example were to include the DATE of EVERY OTHER letter, writing, newspaper clipping, or otherwise "correspondence" that was addressed to George III, or the House of Parliament - the word would remain a non-countable, "mass" if you will, word under this context, which is the most generally used and common occasion for the use of this word.

It would never read:

"The Office of King George III, Sovereign over all British Peoples and Nations, acknowledges receipt of correspondences dated 4 July 1776, 17 September 1787, etc. Dot Dot Dot, you get the idea...."

NOR SHOULD it read:

"The Office of King George III, Sovereign over all British Peoples and Nations, acknowledges receipt of a correspondence...."
NOR:
"The Office of King George III, Sovereign over all British Peoples and Nations, acknowledges receipt of the correspondence...."
The example (regarding Boston Tea Party influenced correspondences) that xavier uses, however, does still have the implication of "connections" and not strictly discussing letters, but many letters of "COMMUNICATION" between people, thus multple communications between multiple parties would be just as easily written communication, or correspondence, as it would communications, or correspondences. It is not really describing the letters or mail themselves/itself; rather, it is describing the intangible connection that these letters created, thus you can have plural of such intangible connections.

THERFORE: In this case, "Who's right?": You. In this usage of the word, you would do well to not dilute the general English speaking public with adding an 's' to the end of the word, even when plural letters may be described. It is still "correspondence" - with no 's' at the end. In this case, your co-worker is not describing her correspondence correctly if he/she is describing any number, singular or plural, of letters or mail, etc., etc., as correspondences.

BUT: Your co-worker is actually correct, though indirectly - benefiting from circumstantial accuracy on a subject they, perhaps, have not understood prior to making their assertion.