If Booker peacefully moves to a location and the owner doesn't initiate combat right then, can that player then buy units in Booker's location and then attack him without moving units into the location? All the combat rules seem to imply combat is specifically initiated by moving.
Yes, you can engage him without moving. The Combatting Booker rules on p14 do seem to imply that the only situation in which you willingly engage him while not-Aggressive is after you move into him, but that appears to be just them using the most common situation to illustrate how the rules work. If you read the Combat paragraph in the Player Turns Phase on p12, you will see that even though Combat always occurs after Move, the only requirement for you to engage is for there to be enemy units in the area (and Booker counts as one).
You will also notice that Undertow can create battles without movement on your part.