I've managed to receive Hyatt points for an Avis rental. I was rather surprised...

But in general, the actual agents at car rental locations seem to be completely awful at handling miles/points from anything other than the most well-known airlines. Frequently, whatever you enter during the reservation phase doesn't show up on the actual rental contract. So you need to reconfirm when picking up the car, and then trust that the agent hasn't entered some completely random airline/hotel code in the appropriate field.

It's also worth noting that Avis are particularly bad. I won't go so far as to say scam or fraud, but Avis ALWAYS find a reason to deny bonus miles. It doesn't matter whether I insist that I followed their instructions precisely, they will always say I didn't.