I'd be tempted to say "There's a HUGE difference between being poor and being low class. Class has nothing to do with the amount of money someone has..."
HUUUUUGE POD. Prime example, of course, being the "lady" in the OP's example...
I've known people IRL who have VERY classist ideas. My mother was one of them, which always made me roll my eyes because my grandparents were NOT rich people, rather they were good, down to earth middle class folks. Same with my other grandparents. My uncle said at my grandmas funeral that when they would ask her if they were rich or poor she'd say "We're rich because we have each other" and I remember they both treated everyone equally.
But I always knew that my mom did NOT approve of DH and why? He's from a middle class family. MIL says she remembers when my mother first saw their current house maybe a year after they moved in. IL's live in a 2br, 2bath Cape Cod. It is not a big house, but then it's just the two of them and that's just what they wanted, was a small house with one guest room and a basement for their dogs to stay in, and they loved this one. My mom came in and really looked down her nose at just how small this house was. And WHY would ANYONE live in a small house if they could afford a bigger one? They MUST be poor!! Oooh I wish I'd known the "That's an interesting assumption" line then!