I don't know whether there's any truth to this or not, but I think it's doubtful that the Beatles had anything to do with it -- they didn't tend to be involved in the sheet music versions of their stuff.

I'm one of those who doesn't really enjoy the whole "singalong" thing, either as a performer or as an audience member. But I tend to think it's more likely that G is "the people's chord" because it's easy to play, not because it's easy to sing. I'm not sure there's a universal easy-to-sing key.