Consider this advice from the Chicago Manual Of Style online:
Q: Dear Editor, I am editing a quarterly bulletin for a church, and have run into a problem. “It’s” is confused with “its” in a lengthy article an author quotes in his text. Given your feeling on the overuse of “sic,” I’m wondering how best to handle this. Simply ignore it, or “sic” it? I appreciate your help. Thank you.
A: A bit of quiet copyediting is best in cases like this, where sic would serve only to embarrass the original author and as a result reflect poorly on the current author as well.
Granted, that's only one source but it at least shows that it happens sometimes. I also find the emphasized part interesting.
Also consider that [sic] is not required. It is an aid to the reader to let them know that the mistake was on the part of the original speaker and not the author. I find very commonly that folks just leave the grammatical mistakes in the original quotes with no associated remarks.