I think that a Vulcan's aversion to being referred to as human could also very well be as differed as a human who might be considered Vulcan-like by other Vulcans.
Remember in "Unification" when Spock comments that Picard has a Vulcan-like quality of logic and dispassion? Were Picard to have heard that, he would probably have taken it as a compliment.
Now, McCoy on the other hand, in times where Spock or even Sarek might have admired the good doctor? He would probably have a conniption if he heard them refer to him in any way as Vulcan-like.
The thought had occurred to me as well in the past, per the OP's question? Did Kirk unintentionally insult Spock? Unintentionally, perhaps. But, Kirk was also placing Spock in a very high regard in that, were Spock truly, fully human, he would've represented the very best of humanity.
I have often wondered, were Spock to become remotely curious about his eulogy:
SPOCK and KIRK are reviewing the funeral proceedings of Spock on a video monitor in Kirk's quarters.
Kirk (on screen): We are gathered here, today, to pay final respects to our honored dead. And yet it should be noted that this death takes place in the sunrise of a new world....a world our beloved comrade gave his life to protect and nourish. Spock did not feel this sacrifice a vain or empty one, and we will not debate his profound wisdom at thesse proceedings.
Spock: (murmurring) That is wise.
Kirk simply grins. Spock will be Spock.
Kirk: (on screen) Of my friend, I can only say this:
Spock raises an eyebrow in curiosity.
Kirk: (on screen) Of all the souls I have encountered in my travels....his was the most.....human.
Spock's eyebrow lowers, and he simply turns to Kirk.
Spock: Jim?
Kirk: Yes, Spock?
Spock: You are not invited to my next funeral.
Kirk: (with an understanding grin) Live longer, and prosper more than I, my friend.
