How would she have known 'how rich' he was unless Nick told her? She wouldn't know from his house. It's an average middle class house. But it's a house he didn't even buy himself. His mother bought it, using money she inherited from his grandpa.
I'd be embarrassed to tell people that all the money I had was earned by somebody else. That I'm a loser who's completely incapable of earning a living. And that although I was once fortunate enough to luck into a role that earned me a million dollars in a year, due to arrogance and stupidity, I pissed all of that away.
Only a mong would be impressed by Nick. And while most public sector employees are indeed mongs, I don't believe a single one would be impressed by how rich Nick's mom is and how big an allowance she gives him.