Because she did a great job on the stage. That proved her deserving. If she was awful and had won, then that means she wouldn't have deserved the award. i.e. IMO, Take Me Out did not deserve the Tony.
"Do you know what pledge time is, Andrew"? said the PBS Executive.
"Yes", Lloyd Webber replied. "My 50th birthday special must be one program that gets done a lot."
"No", mused the man from PBS heedlessy. "Not so much. Our Stephen Sondheim Carnegie Hall concert. That's a big one."
Spoons, forks and knives seemed suddenly to suspend their motion in horror, all around the table.