The R&R HOF is pretty dumb, but it seems to be based on a legitimate voting process - there's a committee that comes up with the nominations and then "Ballots are then sent to more than 900 historians, members of the music industry and artists..." It's more akin to the WON HOF than anything else.
And in recent years there has been a fan poll, and the people who are already in get a vote too.
As far as WWE's go, I cannot imagine anybody else outside the McMahon bubble having a say who gets in. Which I'm weirdly okay with, it's in line with how the company has always operated.