I think I will also encourage DS1 to pursue friendships more with the friends who reciprocate his invitations to come to our place for playdates and birthday invitations rather than this boy. Is this unreasonable? DS1 still says he is a good friend though.
The problem seems to be with this boy's parents not the child himself so I would let it be. I try not to get involved with my DS's social lives beyond asking friends for play dates etc when they ask me to.
That said, if he says no to play dates there's no harm in inviting other children who will say yes.

BTW, I'm the parent who never chats much at school. Nothing to do with the other parents who are all lovely people I'm just a tad shy and anti-social (on a good day, on a bad day I'm positively misanthropic).