I don't have an answer to the OP's question about the rules, but I can share an experience. I was on a CO flight to CLE a few years ago. It was either two or three days before Christmas and CLE had just begun to clean up after a blizzard that dumped literally two feet of snow on the runways. The flight was the only flight from my origin to CLE that day because all other flights had been cancelled; as a result, the flight was completely full (it was a 738).

The flight landed at CLE about an hour late, at 9:30 pm. There was so much snow on the taxiways that they only had been able to clear very narrow paths on the taxiways. In addition, there were many snowdrifts created by the rush to clear the taxiways and reopen the airport - these drifts obstructed access to some of the available gates. We waited on the taxiway for an unobstructed gate to open up; this took about 45 minutes and the passengers were becoming grumpy. The snowplows had cleared a path wide enough for an aircraft to taxi into our gate area, but there were many large snowdrifts surrounding the path.

For whatever reason, the pilot turned left, prematurely, toward the gate just before the path cleared by the plows. The result was that the aircraft became stuck in the snowbank, just like a car in heavy snow. The crew revved the engines several times to no avail. In the end, we waited on the aircraft nearly THREE hours as they tried to dislodge the aircraft using tugs and the aircraft's own engine power. In the end, it took a tug with the engines revved to what sounded like nearly full throttle to move the aircraft out of the snowbank. It was clearly a case of pilot error.

The passengers were furious - many demanded several times to be let off the aircraft immediately. Keep in mind that we were about 15 feet from the gate. The woman next to me started crying on the phone with her relative who was supposed to pick her up. One person called a local news channel and told them that the crew refused to let them off the aircraft. After one of the failed tug attempts, the lead FA made an announcement that we would have to continue to wait while the ground crew determined how to proceed. That announcement prompted a woman to scream, "Let us off this f***ing plane, now!!!" The flight attendant came back to speak with the woman, and the woman demanded that stairs be brought to the aircraft so that everyone could disembark. The FA said that they could not do that because it was too dangerous, but it was apparent that none of the crew had any idea what was going on.

Also, we were given no food or beverages during our four hours on the ground. They did allow people to use the restrooms, however. I don't know what our rights were with respect to disembarking, but I was sent a nice voucher about two weeks later after I filed a complaint.