You apparently use the word "obvious" rather differently than I do.It's an obvious connection. Lightning storm in space = lightning storm in space. We're not talking proof, just the basis for Kirk's guesswork. The point in this case is that spatial proximity had nothing to do with it.
Seriously, this was one of the bits that actually really bugged me about the film. Let's burrow down into it for a moment.
The likelihood that a trained Starfleet bridge officer would describe a spacetime anomaly with such an awkward and unscientific phrase as "lightning storm in space" seems remote to me in the first place... but okay, the Kelvin was in the midst of a developing crisis, that's what it looked like to him (if not really so much on screen), we'll let it pass.
Now, the likelihood that a completely different (unknown) person in a completely different place 25 years later would apply that same awkward terminology to another anomaly (even though the phrase was apparently completely forgotten by everyone except Chris Pike and those who had read his dissertation), and moreover that Starfleet would pick up and disseminate that precise description of the event rather than anything more accurate or useful, seems radically remote.
That the two events described by this inelegant phrase by two different people in two different times and places would actually turn out to be related events seems almost comically unlikely.
Thus, for Kirk to leap to the conclusion that they "must" be related (when even Pike, who wrote the dissertation, didn't), would seem to me evidence that far from being insightful, he was more likely completely delusional at that point. And for him then to assert that they must be connected to two other near-simultaneous events many light years away from the new "lightning storm" would only underscore that conclusion. That Spock (of all people) instead declared his reasoning "logical" is just one of the many indications that this film's screenwriters don't really grasp what logic is.
I understand that one of Kirk's greatest assets is supposed to be his keen intuition. I've seen and read quite a few scenes over the years that demonstrate that asset dramatically and convincingly. This was not one of them.