The agent and me, at DL in SLC a while back:

"Our next flight to Calgary leaves at XX. We can put you on that one. You'll get in about three hours later than you were scheduled."

"I'm meeting friends who live in Calgary and we're driving to Edmonton. We can meet there instead. What do you have to Edmonton?"

"How about a YY departure?"

"Sounds good. I'll take it."

Bottom line is that they have a great deal of flexibility in what they book you on. If you can make a reasonable ("reasonable" depends on the agent and his/her frame of mind at that moment) case for nearly anything, they can do it. The usual rules are only that.

A side benefit is that, with some airlines, rebooking often changes your fare class in a direction that's more favorable for earning elite status. Not always, it's not something one should count on in planning a qualification strategy, but it's nice when it happens.