At some point, you have probably heard the phrase, "you can't prove a negative." It's not quite right. I don't want to get into a debate on the nature of proofs and disproofs in mathematics, which is where proofs actually occur, but we can prove and disprove lots of things. In math.
Outside of math, we don't really prove or disprove much of anything. Rather, we rely on the scraps of evidence we can gather. Scraps of evidence are either compatible with Explanation A or Explanation B, if A and B are mutually exclusive and exhaustive. However, if Explanation B is basically "nothing is going on, move along folks, nothing to see here," then the question is, what evidence would be directly suggestive of it?
And that is the philosophical problem referenced in the famous aphorism.
Suppose that Trump is being influenced by Russia. What would we observe? Lots of contacts. Check. What else? Attempts to loosen sanctions. Check. Refusal to confront aggressive action. Check. There should be deeper stuff. We should investigate. Clearly right now, Sessions can't be the guy leading the investigation. The fact that he failed to disclose meetings, plural, with the Russian Ambassador means he really can't be anywhere near the investigation.
From a criminal standpoint, there is a difference between lying under oath and perjury. It's only perjury if it is material. The concern was about Sessions' behavior as a Trump surrogate. If Sessions was acting as a Senator rather than a Trump surrogate, then he was not perjuring himself, as I understand it. He was just lying under oath. That's why Bill Clinton didn't perjure himself. He was just lying. Of course, now that the shoe is on the other foot...
Anyway, suppose that Trump is not being influenced by Russia. What evidence would directly suggest that? Um... Uh... See the problem? Everything we have observed is also compatible with the notion that Trump can only get it up by thinking about Putin, and if he is not influenced by Putin, but just in love with Putin, then there is nothing criminal. There is a contingent in the Republican Party who have been Putin-worshippers for a while because they are ironically hot for the gay-basher, but this is all compatible with everything we have observed so far. The question is: what evidence would directly suggest this? Actual, hand-written love letters from Trump to Putin? Yes, but c'mon. We aren't going to find those. That's the problem.
This was, ironically, the McCarthyism problem. The accused couldn't prove that they weren't communists. This is why we have a legal system built around the presumption of innocence. Of course, the circumstantial evidence continues to pile up that the connections between Trump and his people are beyond what they say at any given point in time. And we are less than two months in. Drip, drip, drip...
Epistemologically, though, Trump is already fucked.
(Where else do you get sentences like that?)