Well, he's hardly going to admit to knowing nothing about ETs and having no influence on what they do.
Such as position would give him nothing, no influence. No evidence is a much safer line for him to stick to.
Because if he says there is evidence, but cannot explain it, he looks like a Genghiz Putz. Hardly a viable position for the President of Russia about to sit down for a re election.
An opponent could just say "Aha! I know what that is. It's not the CIA, it's aliens fucking with your head" and could not be rebutted. Also, unlikely they could show evidence without turning up with an alien to a press conference, and we all saw what just happened in Pakistan in regards to an internet blackout.
And let's be fair here, Russians and American politicians share the same "we can't be seen as weak" position. Or maybe not weak so much as unable to cope.
I think they're both going to cope just fine. Although maybe not in ways that are obvious to most people.