OP, who knows what these kids may or may not have said. They are kids. You however, are not. You definitely come across as seeking confirmation bias and seem hell bent on whipping up a MN fury about these people - sneaky tax evaders, kids independent school, SAHM, inheritance. Well, so what? There was absolutely no need to mention these details otherwise.
Jealousy is a green-eyed monster, no matter how you dress it up.
I would almost guarantee that your kids have already picked up on your sentiments about this other family and are telling you this because they think it’s what you would like to hear.
If you are fired up enough to post some little kids “he said, she said” thing on the internet, you are probably none too subtle about your feelings in real life. Even if you haven’t directly mentioned this to your kids, they will know. Chips the shoulder are usually visible from miles away and to anyone and everyone who knows you.
I’m sorry to be blunt, but just let it go. You will never know what was or wasn’t said. If I were you, I’d be more concerned about letting your own insecurities influence your own children. The other children are not your concern and never will be be. Break this cycle and stop focusing on other people. Then your kids will do the same.