I can't believe that there is actually a discussion of "evidence" and "proof" going on here about what was Kirk's first command. I love to debate Trek minutiae as much as the next guy but, c'mon, this is a freakin' work of fiction. There is no truth about Kirk's first command because Kirk doesn't exist.
But the thing is -- and I think maybe some posters here are overlooking this -- that "evidence" and "proof" are two very different things. Evidence is simply data that you gather and use to try to arrive at a conclusion. It literally just means "that which is seen" -- it's an observation or result, a data point to be taken into consideration. Proof -- which is more of a vernacular or legal term that you won't really find in scientific usage -- is decisive
evidence (or indisputable reasoning, in the mathematical or logical sense), something that leaves no doubt about a certain conclusion.
So calling something "evidence" does not mean it's conclusive or even indisputable. It just means it's data that can be used to evaluate the question. Evidence can support a certain conclusion without being enough to prove it, because of course it usually takes more than a single piece of evidence to arrive at proof beyond a reasonable doubt. If you find the butler's fingerprints on the murder weapon, that's evidence in the case, and it can be taken as evidence in support of the hypothesis that the butler did it; but if you gather more evidence demonstrating conclusively that the jilted lover has gunshot residue on her hand and left her DNA at the scene and drugged the butler and put the murder weapon in his hand, then you've proved that the jilted lover did it. The fingerprint evidence is still evidence, but when placed in the context of the rest of the evidence, it contributes to a different conclusion than it suggested by itself. So evidence and proof are not the same thing. Evidence is data that's open to interpretation; proof is a pattern of evidence that is only consistent with a single conclusion.
So you're absolutely right that we can't talk about proof in a case like this, but we certainly can talk about evidence. Dehner's line is certainly weak evidence, and in the absence of any further evidence its probative value is too limited to allow any firm conclusion to be drawn. But it is perfectly valid to call it evidence. This is just one of those cases where the available evidence is insufficient to allow a definite conclusion -- something which actually happens pretty often in this world.
But the scant evidence we do have does seem to make one conclusion more probable
than the other, and in this case, where there will never
be any more evidence to allow a firm conclusion, probability is the best we can ever do. And since it is just imaginary, probability and common sense are good enough for me.