I haven't RTFT, but just wanted to speak from the POV of a "richer" parent in this scenario:
My DS had a great friend, "Adam," when he was in primary school. We had Adam over for many playdates; he was a really nice kid and he and DS got on very well.
Never, ever did DS get invited back to Adam's house. (DS was a very inoffensive and well-behaved kid, so it wasn't that. Other parents used to comment on his good manners when they'd had him over for playdates.)
One time we were dropping something off at Adam's house and DS was SO EXCITED just to see the outside of Adam's house and see Adam waving out of the window. It broke my heart so much that I later had a slightly awkward conversation with Adam's (very nice) mum where I mentioned how much DS would love to have a playdate at Adam's house sometime. Later that month they had a playdate there and apparently had an awesome time. There was never another playdate there, though.
No idea whether this was the reason, but Adam's house was weeny compared with ours. DS obviously didn't care (what kid does?) and nor did I. It wasn't till long afterwards that I read a similar thread to this one on Mumsnet that I started thinking that maybe Adam's family did care, and that had been the reason. Bluntly, we just had a lot more income and property than them (they worked in very cool but low-paying arty jobs).
Anyway, whatever the reason, what I really remember from that time is how sad it was for DS never to go to his best friend's house, and how massively happy he was when he finally got to go there. It was incredibly touching how made up he was to finally see Adam's bedroom! and Adam's books! and meet Adam's cat!!
So maybe the parents of your kid's friend are a bit money-orientated or snobby (or maybe not). But I've got to put in a word here for your kid's friend. I'm pretty sure he would love to come to your house and it might mean a lot to him if you invited him.