Well, he was Chief of Starfleet Operations, so by analogy with the U.S. Chief of Naval Operations, he should've been in charge of fleet deployments, operational efficiency, crew assignments, asset allocations, and fleet repairs/refits. That would've put the refit under his purview to an extent, but it would've been just one of many, many responsibilities he had to juggle, and he wouldn't have been the guy directly supervising it, any more than the U.S. Secretary of Transportation is directly managing any given highway-repair project.
Besides, Frontier Doctor doesn't just have him generally overseeing the project, it has him managing it on a detail level, running simulations to fine-tune parameters as niggly as the line of sight from the command chair to the defense station. In TMP, he didn't even know that the phaser power circuits were routed through the warp engines. There's no way he could've been that ignorant of the ship's systems if he'd been such a hands-on participant in the redesign. And as CSO, he was responsible for every ship in Starfleet. He wouldn't have had time to micromanage any single ship's redesign. He would've had someone under him who was responsible for that. Heck, TMP established that he hand-picked Will Decker for that job.
