Unless you are just making the point that YT censorship is more acceptable than government censorship (which I think everyone agrees with), then I'm not sure how you can have your cake and eat it to here.
But if you run a forum and say you will not allow any view to be expressed therein that you don't agree with, you aren't in fact "allowing people to make up their own minds"---unless by "allowing people" you just mean not actively harming them for expressing views in other places, or something equally wild.
Another way of saying it is that no one would say you are "tolerant" if you only "tolerate" behavior you agree with.
I think you're missing their argument. YouTube censoring doesn't prevent information from being published elsewhere.
(Sidenote: I do think YouTube and other corporate-run forums like that would welcome some regulation in the area, for two reasons: (1) they'd no longer be blamed for how they decide difficult content questions, and (2) it might make it more difficult for small startups to disrupt this space by increasing the legal barriers to entry.)