The funny thing is, cryosleep ceased to be used in insystem, sublight applications in the early 21st century, a valid reason for Kirk to remain fairly ignorant of them. But apparently they were still used regularly enough in outsystem, FTL applications in the early 23rd century. Why is Kirk ignorant of such a recent practice? He would probably have encountered examples of it in his training: if colonists were using it as late as 2210, Starfleet would still have to be capable of handling a colony ship emergency involving cryosleep around that time, and would probably retain the skill for at least half a century afterwards.
We can naturally assume that Kirk wasn't ignorant, and that McGivers merely assumed that he would be, hence her lecture. But why would McGivers in turn be assuming such a thing if cryosleep (or other techniques for suspended animation, regardless of the specifics) were a recent thing?
And McCoy did seem to be slow in coming to the conclusion that the "alien", low heart rates heard aboard might come from humans in suspended animation... Although this might have to do with differences between Khan's suspended animation techniques and the possibly more modern ones involved in, say, the 2210 mission.