Picard was born in 2305, and (I believe) Kirk first took command of the Enterprise in 2265. I can't find anything on when Jean-Luc's father, Maurice Picard, was born, but just based on Jean-Luc's year of birth it's doubtful his grandfather was still in diapers by the mid-2260s. Possible, but probably not likely.
Still, I think it's just best to not take the line literally. I highly doubt Kirk knew exactly how old Picard was when he said that. He was just saying that he'd been in the business of saving the galaxy for a long time. But when you think about it, that doesn't really mean much since he'd spent the last eighty years in the Nexus, during which Picard had amassed nearly forty years of experience as a Starfleet captain himself.
Good point. In fact at that point Picard was in fact arguably older than Kirk, who was about 60 when he entered the nexus, as opposed to the ~66 year old Picard.
Anyway you slice it, Picard could make a claim to be more experienced as a starship captain:
Kirk had for sure one 5 year mission, and some fan speculation that he commanded a second. Let's be charitable and say he did. Add another ~7 years on the "A" and that brings it up to ~17 years commanding a starship at retirement. That doesn't even come close to the 22 years Picard had on the Stargazer, let alone if you add 7 years on the "D". There's also that nine years in between when he was doing God-knows-what, but I'm inclined to believe he had one or two other commands during those years, just because going from an very old ship, to no ship for nine years, to a massive new ship seems rather unlikely.