You weren't wrong at all! They moved their office and you got there in an appropriate amount of time IMHO. 10 minutes is not that late and like everyone else said, it's way less time than you usually wait in a Dr.'s office to begin with. They shouldn't schedule people that close to quitting time if they're not willing to see anyone that close to closing.
What if you had to get a babysitter and get out of work just to make it to the appointment? It makes me mad and it didn't even happen to me. Can you imagine if next time they make you wait longer than 10 minutes and you say "I'm sorry, I can't see you today because now I just don't have enough time to do everything else I was supposed to". I'd say find a new doctor but most are like that
