It says in the rule that you can only do an action once per round, but for us this refers more to the rule that you have to take all discs from an action spot when performing it.?Where does it say that? The closest thing I could find is the rule on page 7, which says that each character-tile's bonus may only be used once per round.
I agree that allowing players to do an action twice in one round (via the governor) is dubious from a balance perspective. On the other hand, I haven't found a rule against it.