The short answer is "DM's Discretion". However, there is reasonably strong logic to support @PatLudwig's ruling. I arrived at this conclusion after some e-mail discussion with Wizards of the Coast's Customer Support.
When I asked about this issue in the support request, I used
Grit and Spittle [ddi] as an example power, as it does allow you to make a saving throw as a
Effect: You spend a healing surge but regain no hit points. You make a saving throw against every effect on you that a save can end.
This was their first reply:
As long as the Dazed was removed during the turn (and not at the end of the turn with the automatic saving throw), the creature will get the full compliment of actions. In the case of your example, they will still have a standard and move action left.
The response unfortunately did not provide any rules quotations that specifically address this scenario. When asked for one, here is the reply:
I'm not sure there is a specific ruling that describes this situation. I can arrive at it in a roundabout way, though. The text for the Dazed condition from the Rules Compendium is:
"The creature doesn't get its normal complement of actions on its turn; it can take either a standard, a move, or a minor action."
By this logic, when you are dazed, you can spend your action to use Grit and Spittle to make (and succeed) your saving throw. At this point, the game checks if his turn is complete. Because it is after the power has resolved, the game sees the character as not dazed and only having taken a minor action, so his turn doesn't end.
I did send a final reply to WotC, requesting that they submit the issue to R&D for an official fix.