If the Enterprise had been the only Constitution class starship to return, then it would be easy for Kirk to boast about having the best crew—because it would have been the only starship crew in the fleet!
The funny thing is, Kirk doesn't really boast about his crew all that often, and he basically never praises his ship. It's really only in the desperate pep talk he gives to a dying crew in a dying ship in "Immunity Syndrome" that he stoops to using the expression "the best crew", along with "a good ship"...
Back in the time of TOS, Kirk, his crew and his ship might not have been anything special. That doesn't mean they wouldn't have become unique by the time of ST:TMP somehow, possibly indeed by the virtue of their we-survived-the-full-five-years t-shirts. And indeed we hear rather explicitly that this five-year mission thing makes Kirk uniquely qualified among all Captains or or flag officers currently on Earth
to face the V'Ger threat, so it must be a rare achievement indeed.
That is, if we take Kirk's word for it; for all we know, he bought the permission to command the Enterprise
with hard cash.