It's from The Making of Star Trek. I don't want any more cracks about The Book!
Doug Drexler calling TMOST "The Book" like he was in "A Piece of the Action" was probably my favorite moment in the 50th Anniversary Special.

I think that's how I'm going to think of it from now on.
And it's implied in the second pilot. "Gary told me that you've been friends since he joined the service, that you asked for him aboard your first command." That would be an oddly distant way of phrasing it if the Enterprise had been his first command. Implicitly, Dehner is referring to a different ship.
I think the dialogue is ambiguous enough that it could be interpreted either way, much like Kirk's "There are only 12 like her in the fleet" statement in "Tomorrow is Yesterday." But I agree that it does make a certain amount of sense for Kirk to have commanded another, smaller ship before the
Enterprise.
I don't see how that's awkward. Given how much changes between the end of TMP and the start of TWOK, it would be more awkward if only three years passed between them in-story. I mean, it's not just Kirk going back to the admiralty, Spock becoming a captain, the junior officers getting promoted again, and Chekov getting promoted twice and transferred to Reliant. It's all the changes in the setting itself. The ship that was brand-new in the last movie is now a training vessel. The uniforms have changed yet again. The crew is a lot less diverse. The feel of Starfleet as a whole is a lot more militaristic. Bringing TSFS into it, we have Morrow running Starfleet instead of Nogura. All that makes much more sense (relatively) if there's 10-12 years between movies.
I agree. I personally would love to see a few more stories filling in the gaps between TMP and TWOK (and even a few between TWOK and TSFS). Did the entire crew stay on the
Enterprise for the next five-year mission? Why did McCoy choose to stay in Starfleet again? Did Chekov transfer directly to the
Reliant, or did he have another assignment in between? When exactly did he get promoted to Lt. Commander and Commander? Did Sulu or Uhura feel odd about suddenly not being Chekov's superior officer any more? Why did Kirk decide to give the Admiralty another try? Was Sulu really in line to command the
Excelsior before the political fallout from Genesis happened? What happened to Nogura and why did Morrow take over? And what happened to Morrow after TSFS? Was Kirk stealing the
Enterprise too much of a political embarrassment for his administration?
There have been a few stories offering answers to these questions, but I'd love to read a few more. The thing I find tantalizing about the movie era is that we really only get limited glimpses into the crew's lives every few years with only a few inferences as to what happened in between.
That puzzles me, really. Why would people assume that the Enterprise was Kirk's first and only command just because it's the only one we knew of? The Enterprise was a capital ship, one of the most powerful and important ships in the fleet. They wouldn't give a command like that to a novice captain, as a rule. It's just logical that he would've gained command experience on a smaller ship before being judged worthy of commanding a heavy cruiser.
Maybe they think that seeing a young Kirk commanding another ship might be confusing to casual fans? Heck, it's why we got Morrow's "The
Enterprise is 20 years old" line in TSFS. People might wonder why the
Enterprise is so special to Kirk if it wasn't his first command.
The way I rationalize it in my head canon is to imagine that Kirk assumed command of his first ship while he was still a Commander. That way the
Enterprise can still be a bit special by being the first ship he commanded after his promotion to Captain (It keeps Kirk from being promoted to Captain too absurdly young, too).