Earlier quoted context omitted.
All the big hotel chains will usually give ~5% off for reserving directly since they pay ~15% to OTAs. They will require you to be a “rewards member”, but that is just checking a box since you already have to give them your personal information.
I got the feeling that it's the opposite. We pay the Booking fee. I've had hotel receptionists give me their card and say "If you come back some other time, just call to reserve directly with us, so you can save the x% that Booking charges for your reservation!"
The hotel has a room they want to sell for $100 a night. They can list it on their website for $100 a night, and after paying credit card processing fees, they get to keep the remainder.
The hotel now lists the same room on one of the booking sites that charges a x% fee for facilitating the transaction and providing discovery for the hotel (getting the room in front of interested customers). The hotel can either take a x% haircut, or charge x% more. So that same room might be $110 per night now instead of $100.
It's a business decision, and not all operators will make the same one, naturally.