I could be wrong, but I suspect this is actually a problem with processing the transaction itself. Processing in the way that AirBnB does is typically frowned upon within the card processing industry from what I've discovered.
The processors and the banks have the power and can shut a merchant off if they determine that they're not playing by the card association's rules. The method that AirBnB employs is referred to as Third Party Payment Aggregation. They're processing payment on behalf of the hosts.
Venturing into this territory for an established company would likely cause a lot of pain. They might need to establish a relationship with a different processor and/or bank who would support the model. If they were to switch without first talking to the bank and processor they would likely be shut down quickly for violating the terms of their agreement. So it's not as simple as a relatively minor product pivot for VRBO.
A smaller startup can risk a lot more by carefully walking the line of what the bank/processor/association will accept. But they're still at risk, I believe. Unless maybe they have found some way to mitigate much of the risk (I can think of one or two that would be possible after building brand recognition), I'm not sure.
So I think you're right with your last paragraph but I think it has more to do with Credit Card regulation than hotel regulation... but I don't know anything about operating a hotel.