I believe you are correct. Spock states in that episode:
SPOCK: A few hours ago, the Captain elected to remain on board the Defiant so that three members of this crew would have the best chance of returning safely to the Enterprise. His concern was not only for them, but for all the members of the crew of this ship. You all know the sequence of events. We were fired upon by the Tholian ship. At that time, Captain Kirk may have been alive. I deemed it necessary to return the Tholian fire for the safety of the Enterprise. The Tholian ship has been disabled. But as a result of the battle, we must accept the fact that Captain Kirk is no longer alive.