I don’t see the problem. If the story explains how the characters came together as they are "later" seen (without obvious inconsistencies), its an origin story.
And that's pretty much what Star Trek or Batman Begins are. The characters are almost exactly the same as what the audience knows of them.
Otherwise it’s a reboot, new beginning, alternative history, displaced history, etc. etc. etc. What’s so hard about that?
Those are really just sub-classifications. The case could be made that a reboot can be an origin story depending on your definition of origin story (and reboot for that matter).