...Or whatever he did after losing the Stargazer, as these feats supposedly would have been essential in him getting the Enterprise. The Stargazer career as such doesn't sound like a recommendation: 22 years stuck on the same ship (with some of that spent commanding her), then an embarrassing loss of the vessel. And then the disclosure that the vessel had in fact fallen in the hands of Federation adversaries, or at least competitors, before the offer for Admiral rank came!
I dunno, 22 years sounds like a pretty impressive resume to me. It's pretty much indicated that the Stargazer was involved not only in general several exploration and scientific missions, but also was part of the Federaton/Cardassian border war. Not to mention Picard's having made first contact personally with 27 species... chances are a good number of them were on the Stargazer. So plenty of chances for him to have been a hero there. Sure the end of the Stargazer's career was less than glorious, but one screw up doesn't undo 22 years of good.
Picard spoke nostalgically of the ship quite often, going as far to call it his "first love" to Scotty. So I could conceivably see him turning down better commands to stay with his old warhorse, finally only taking a new command once he had lost her.