In my eyes, enough due diligence was provided in finding out the person told you they were 21. It's not like you didn't have a number to go with (falsified or otherwise). Technically, being told someone is 21 and then having sex with them, only to find out they are 16, is entrapment.
I don't think it'd fall under entrapment unless their sole purpose in engaging in the acts was to get you in trouble.
I could be mistaken and I don't know where but I remember reading the case of a guy that got convicted and the girl either told him she was of age or had a fake ID or something.
It might have been one of those cases where she was in a bar so the "legality" assumption was there.