Can passenger distribution cause a parked airliner to tip?
It's possible. 

When FedEX used 727s a lot they had regular occurrences of cargo being loaded too far back while the front was empty. The airplane would sit on it's tail. Not usually damaging but having the front door quite a bit higher than usual was an issue. If no one was on board it was awkward to get it back to normal, and FedEX really doesn't like delays. At my airport in the 90s you often saw a post attached to the tail while they ere loading.

Highly unlikely a 747 will rise up like a bucking horse, but it is possible that you can take enough weight off the nose gear of something smaller that the strut can extend. This would make the cabin door rise by about a foot, probably hit the jetway, and upset most everyone onboard. What would the passengers probably do? That's right - run downhill.