The latter point is a claim in the Wolfire case, and is supposedly a term in the Steam Distribution Agreement which all publishers sign. It’s behind an NDA, though.
There is indirect evidence of this in the following: if Steam’s cut is 30%, and Epic’s is 12%, and a publisher’s own site has no platform fee… Why don’t we see gradiated pricing across these different services?
It seems like there must be some policy or threat of consequences that keeps a game’s price consistent.