While I’m no fan of paid sponsorships holding back good games, this is untrue.
Neither nvidia nor amd block their partner devs from supporting competing tech in their games. They just won’t help them get it working, and obviously the other side won’t either, since that dev is sponsored. There are some games out there that support both, some of them even partnered.
So yes, it’s bullshit. But it’s not “literally paid” bullshit. Bethesda could have gone the extra mile, and didn’t.