What other explanation would there be? That he was Kirk? Sounds way too fantastic to be true.
I mean, Spock would have reason to believe in duplication, and indeed in evil duplication: the dog experiment had already been conducted. But he couldn't let the rest of the crew know that the (evil side of the) Captain was to blame for the attempted rape and possible other nastiness: his position through and through was of protecting Kirk's reputation. Of course he would have to insist on calling the evil Kirk an impostor, an intruder, anything to detract from the facts.
1) That's what a Vulcan would probably do, so would Spock really be suspicious?
2) The good Kirk did not do everything possible; he just sat there and whined. Declaring defeat and leaving might just be another symptom of Kirk being too good for his own good.
3) It's not as if we'd really see Spock being mistaken. He has time to squeeze out one line, and he does that with Vulcan lack of passion, even if he doubts Kirk all the time.
The first two ideas are just idle rationalization. The third is what happens in the scene in the dramatic sense - things proceed fast, and the evil duplicate is immediately exposed, even though he desperately (and rather pathetically, almost gaining our sympathies there!) tries to confuse the issue.
Do we need to know? In-universe, we know he has prepared a nice video-testament that will clarify everything. In-universe, we also know the good Kirk would have been unable to finish even this simple sentence to any degree of coherence, being a wimp and all. But out-universe, all the necessary meaning is implicitly there.
There was supposed to be this devilish side to Spock at first, especially as regards women. Some of it survived till "Omega Glory", a rehash of an unused pilot script.
Even if some of that was toned down eventually, Spock still tries to be a Vulcan. And Vulcans probably beat their wives a lot, unless they don't walk two steps behind their husbands as in "Journey to Babel". Makes Spock all the more interesting as a character...
Timo Saloniemi