I found out something, All starbases can move. Well actually I have only tried it with the TEC starbase. Though it only moves about the speed of a two ton elephent in a pool full of concrete, but it does move.
Try it if you don't believe me. Although I would suggest to give it the move order, see where it is in relation to everything else, then leave it alone for several minutes then come back and see where it is in relation to everything else then. It probably won't have moved far but it will have moved.