Indeed they can, though still subject to their self-imposed two hour or four hour time change refund policy (allowing you to get a full refund if you don't accept the change -- subject to change of course). Of course, with a connection, it is far harder for the time change to be less than two hours (but not hard for it to be less than four hours).That's a good question, expecially if you paid more to get a non-stop, which I just did. I don't think they can re-route you without your permission.
The fundamental take-away from reading the contracts of carriage, for every US domestic airline, is that the only thing you're being promised is transportation from City A to City B on a specific date, in a specific cabin. All other aspects of the reservation -- the flight time, the connections, the seat assignment, the type of aircraft, the amenities, etc. -- are all just requests on your part, just like with a Disney resort reservation when you request a room on a "high floor".
Most of the airlines will work with you to satisfy you, but their obligations are pretty minimal, except for the core aspect of the service, providing you transport on a certain day between two specific cities.