Defense causing runner to lose contact

[JefferMC]

On another board, a conversation has cropped up around a poster positing the following situation:

Runner dives back into bag, hand makes contact with bag, fielder applies swipe tag forcefully enough to cause the hand to lose contact with the bag.

Assuming you see all of this, in this order, is the runner out?

Of course everyone knows that the defense isn't permitted to push a runner off the bag. Don't they? How? I can't find it in the rules that you can't.

So, short of something so obvious that it draws a USC call, what rule keeps the defense from causing a runner to lose contact with the base so they can apply a tag for an out?