It comes down to literal interpretation of the rules. Nowhere in the DMG or PHB does it state that saving throws are considered an action. If they were, you wouldnt be able to make them on other's turns. But, specific beats general, so the rule states that this is an action, and a full-round action. Of course, this is making what is essentially thinking a 6 second long action. ???
I can almost assure you that the spell description is written like that to make sure people play it that way. Nowhere else does it say that saving throws are actions, or full round actions. You dont end your turn dodging a trap in combat. You dont end your turn if you make a save against a Web or Grease spell. And it doesnt take any time out of your turn to do so. It's a specific rule for a specific situation, and it's horribly bad dm'ing to take a specific rule and apply it generally.
If you ever DM, it's your call, but i'd be out of that game.