So if "who" refers to people, and "that" refers to objects, what about the passage in Harry potter where Rowling says something like "the cabinet, whose doors bore engravings..."

I blame Microsoft Word Spellcheck. Before I handed in my essay, all my "whom"s were underlined with squiggly green lines. Spellcheck wanted "who". I thought it was whom, but who am I to argue with Spellcheck? I changed my "whom"s to "who"s and my lecturer marked me down. Spellcheck changes my "which"s to "that"s (eg, "a tradition which has been handed down", spellcheck wants them all to say "a tradition THAT has been handed down" and it sneakily changes some of my British spellings to the American version without even telling me about it. I changed "diaspora" to "Diaspora" because of a squiggly red spellcheck line, got marked down for that as well. Goddamn Spellcheck, demolishing our language!

That would be "department heads".
I work at an English Language college, and nobody believed me when I said it was "mouses, so I came here to look it up. Guess I wasn't as correct as I thought I was.