Can United bump confirmed paying customer?

Can they legally under their contract of carriage? Probably- every carrier will write it so you aren't guaranteed a premium cabin seat with the ticket purchase because they may need to substitute one plane for another or give you a weird rerouting in the event of mechanical or weather issues, and even not all 757 or 767 planes in the fleet will have the same seating distribution.

Is it likely? Not really. Same contract of carriage also likely states that you're due a refund of the difference between the cabin class you paid for and the cabin class you got, and United is not likely to want to give you money back. Revenue is generally going to trump non-revenue upgrades, even from regular customers, and most road warriors get that. (Want First; Buy First as they say on FT)

Any airline can bump any passenger. It is unlikely that you will be involuntarily bumped if you follow all the rules and the equipment stays the same, but it can happen. Airlines will generally ask for volunteers first. They will typically up the compensation until they get volunteers.

I have no specific experience with this on United First/Business, but I've flown plenty of times when bumping was in play.

Honestly, I wouldn't worry about it because it is beyond your control. Just check in on time and do your part and the odds are pretty low that you will get bumped involuntarily.

I agree that it's beyond your control, but I don't think I'd describe it as too unlikely. I've had involuntary bumps several times in recent years, even though I was checking in on time. The most annoying was Delta/KLM less than a year ago – I was called 4 hours before the plane was supposed to take off and told that I was being bumped, and I was one of many. Comparing stories at the airport (Venice), it seemed that KLM had bumped a number of passengers who has booked through Delta and were flying to the West Coast. When I eventually transferred to a Delta flight in Amsterdam, one of the flight attendants said that she had previously seen KLM do this to Delta passengers.

Good reminder to follow check in rules.

If you were travelling from the EU, 261/2004 would apply ie a 75% refund of the ticket for any downgrade. As UA is not an EU carrier it wouldn't be this travelling the other way though (or elsewhere).

If denied boarding completely, the compensation would be €600 plus re-routing plus provision of care.

Adam - that did happen just the other day to a REVENUE first class passenger. I suspect that is what the OP Judy is referring to. If you read the Trip Advisor Air Travel Forum - that has been a hot topic for the past couple of days. The person in question (and a long time TA contributor had 1k status along with his wife) booked FC to London in cash. His wife's seat was given to a Global Service days before the flight and she was dumped off the entire flight (after turning down an economy seat). It's generated a lot of conversation over on that forum.

I realize that this is a discussion of Bumping and not re-seating. But I want to note that when my wife and I had, relatively rare for us, slightly-restricted Business Class seats on Emirates, we had confirmed, revenue seats on the two-seat (window) side of the aisle, Nairobi-Dubai. When we checked in, we had been moved to two middle-seats in the four-across (AFAIR) center section. This was the Emirates equivalent of "Domestic Business" configuration on United, not Emirates already famous A380? luxury business overwater configuration.

When I sent in a written complain, I got a polite but dismissive reply, we have the right to change your seat. They didn't say, "Try First-Class next time."

That guy on Tripadvisor is a long-time and very helpful contributor to that forum. I see no reason to suspect his story. I have no idea what "Global Services" status is on United, but it seems that higher status person wanted the specific seat that Mr. Hunt's wife had reserved. So the Hunts' own status did not come into play at all.