Vulcans are founding members of the Federation. I would imagine that a request from their highest leader regarding one of their own legends would carry some weight.
So then the Federation is really no different than governments today? More concerned with image than truth...
But this whole thing totally discounts that this is a secret that would already have to be out of the bag. Vulcan had been a Federation member for a century, Vulcan traders are not an unusual phenomenon, humans are living on Vulcan and you have at least one human who has married a Vulcan.
Incredibly unlikely that Pon Farr is a secret.