No, if you read the DOT website I linked to, you'll see your second point is not valid either.
The DOT explicitly states airlines are not allowed to deny you permission to board, or remove you from the flight if.... If you have already boarded the plan, or had your ticket scanned, and are not being unruly, airlines are literally not allowed to deplane you.
Trespass law is not within DOTs regulatory purview. It is possible for a request from an airline to be legal under one set of laws but illegal under another. Airports are both under federal and state law. Which may conflict at times.
By that logic a stranger could get into my car if it is parked in the street, since it is a private vehicle parked on the governments property. This seems counterintuitive.
But the vehicle is not parked in a public space it's parked on private property that is owned by the government. If someone is in a vehicle on someones property then it's the property owner not the vehicle owner were trespassing laws apply to.
The Airline is as much a guest in an airport as the passenger is.