Back in my military days, well over 20 years ago, you could take the paper ticket on a government contract fare and walk it over to any airline. I routinely would do that.

Eastern Airlines had a number of city-pair contracts, but Delta would gladly accept the ticket and put you on a Delta plane.

In this day of e-tickets, I have no idea if something similar could be done -- and I am quite glad I don't have to deal with it.