The key here is attitude. While your upbringing influences that, you can always make a choice to be the relaxed rich kid. Even if your parents' income says differently.
From that point on you're never asked for ID. The bartender can tell from your walk, your gaze and your speech that you have it, just like before they could tell that you didn't.
A good friend of mine had his nascent teaching career destroyed when he some confident-looking 20 year old chick dropped a 6 pack of Bud Light on the counter of the store he managed part-time. He didn't bother asking for ID (which he was typically pretty strict about) and was led out in cuffs.
He received a conditional dismissal after 3 years of probation, but explaining a 3+ year career gap ("So, why did you quit teaching after 6 months to fix cars?") takes you off the fast track.
She probably thought I must be 21 because who would throw down proof they weren't 21 in order to get into a 21+ show.
Before that, I worked customer service at a grocery store for a while too, and it got to the point that I could tell who stole something in order to return it by just how they were standing in line waiting, and even if that didn't help, their first few words would give it away. Of course, that didn't mean I couldn't help them. My boss actually was really upset when I told one person to never come back... go figure.