I've never heard of anyone playing it that a person can't charge and grapple. I've also never heard of anyone ruling that in order to move and then grapple, you'd have to have spring attack.
My interpretation has always been that the "move into the opponent's square" portion of the grapple attempt has nothing to do with a Move Action, a 5' Step, or any other type of movement defined in the game. It's a free repositioning granted by virtue of having made a successful grapple attempt. Although this repositioning provokes AoOs if the grappler has otherwised moved during the round, it is mostly sui generis, unrelated to other forms of movement.
That's how this peanut-gallery-member would rule it, anyway. I think the moving-into-the-opponent's-square part of the grapple is far more important than considering the "move-in" portion of the grapple to be normal movement and thereby not allowed in charges, move-grapples, and the like.
Daniel
[edit: looks like Seasong's already ruled the way I was arguing, so this spectator's voice doesn't make much difference. One more issue, though, that you may want to be clear on ahead of time: will this ruling allow someone in rare circumstances to squeeze an extra 5' movement out of a charge, by charging 60' and then grappling someone? I'd suggest yes, just to keep it simple.]