Can they really do that in MLB?

At 24:30 into the movie, Billy Beane tells Peter Brand "Pack your bags, Pete. I just bought you from the Cleveland Indians."

How common is this for the 'baseball ops' people on a MLB GM's staff (up to this moment in the film, the Peter Brand character had been "special assistant to the Indians GM, Mark Shapiro") actually have contracts that can be bought and sold?

That would seem to be a sort of labor-law thingy that would require a union for such front office people, but I've never heard of any such union.

Or is this a ridiculous fabrication that just serves the dramatic purposes of a movie?