I think Trelane said something about Lt. Uhura being captured, presumably as a (negress) slave, and she says: "We are a free people!".
But yes, she wasn't offended by the term. Just made it clear that she was never a conquered "slave".
It was Abraham Lincoln who said that, in the episode where it was bad guys vs. good guys from history [of various planets] but I don’t recall the title. ;)