It also depends on what you mean by ownership.
If you have a Mileage Plus number associated with the reservation, you can see the reservation in the "my reservations" section. From there, you should be able to select seats, apply upgrades, etc. Even if you don't have an MP number, I suspect you can get access with just your PNR and last name, though others may know better.
I have to book through my company's travel agency, but once the reservation is created and ticketed, that's the last time I work with them. I don't know if I have ever tried to change an actual flight by myself, but I always do seat selection, upgrades, and check-in through UA.com