I guess herein lies the problem, as he's Garth of
Izar, potentially a multicentenarian alien. (This opposed to Cochrane of Alpha Centauri, whom McCoy explicitly confirms as a human being.)
This is further complicated by the fact that Garth supposedly took treatments that radically affected his appearance (i.e. he became a shapeshifter of some sort). If he was a wrinkled old man prior to this, then went to the asylum for the incurably criminal, and then when Kirk and Spock arrived emerged triumphant but looking fifty years younger, this would not warrant extra comment - the ability to shapeshift would be impressive enough, and the ability (and desire) to look younger would directly and naturally follow.
So Kirk might be speaking of reading on the adventures of Garth in the old war with the Kzinti 200 years before his time. (The only obstacle on
that path is that TAS, our only source for wars older than 100 years, also says that 75 is the mandatory retirement age from Starfleet, and suggests it has never been higher than that. But perhaps this only goes for humans?)
Personally, I'd like to put as much time between Garth's heroics and Kirk's cadet years as possible, to give credence to the idea that Kirk thinks war is a thing of the past. But that's probably a futile prospect, as Kirk in other episodes isn't nearly as pious about war; for all we know, he's just manipulating Garth here, and his facts may be grossly biased.
Timo Saloniemi