So do you (the gentle reader) think that administering the cure into the water system when it had been refused by the government would be bad?
My personal opinion is a different matter from the letter of the law. All I'm saying is that according to Starfleet regulations, they couldn't deliver the cure if the legitimate government refused to accept it. However, as I said, that would not have been the case here, since the Vidiians desperately wanted the cure. I'm not interested in debating counterfactuals.
And what if (It's not the biggist if in the world, ask the rest of Europe what they thought of Germany in 1945.)the 15 empires surrounding Vidiian space who had been picked raw by raiding parties for kidnies and livers said "No Captain Janeway we would rather you didn't "cure" the Vidiians. At this point we're glad they're dying off and we are relishing their final moments."
It's even possible that the Phage was a weapon that was targetted at the Vidiians for a good reason, and whosoever that was might be miffed that Janeway is interferring in their best laid plans.
It's not a question of permission, it's about the balance of power.