I bet it's one of those things rich people do to their kids. They have enough money that the kids don't "have" to work but they're trying to make it seem like the kids aren't worthless layabouts, like a certain fat person we know. So they make them get "jobs". My brother dated a girl like this. He dad was a millionaire, she got a law degree and she was actually working for one of those Biglaw firms for a while before she decided she didn't like working. Now she opens up boutique shops in NYC, runs them for a while, and then closes them. She's like Betsy Resto selling furniture and baubles but way more upscale. Daddy is happy because she's doing something "productive".
It's the same with Brinton. He chose law so he can spend 7 years in school fucking off and it sounds good at the country club. He doesn't really have to work so he can be a stupid wine lawyer or whatever and take some weird cases (case in point, Rick). His parents can say he's a lawyer, again it sounds good at the country club. They probably just don't talk about Betsy or it's something like "she's still finding her way".