There's no such thing as Standard English, and even so using sat like that is perfectly grammatical.

It's an ellipsis, which means it's perfectly cromulent since the rest of the sentence is pragmatically implied.

There are no words in the English language that can only be used in writing, and not spoken. Furthermore, suggesting that there's a rule that states that something is incorrect in a language when the meaning is transparent is a prescriptivist attitude, and therefore bad and dumb.