According to Mike and Mike this morning, it is standard operating procedure for the refs is to use a pressure gauge to check all the footballs in the pregame inspection.
So it's unlikely the refs missed it beforehand.
So that brings it back to why the league puts the balls back into the care of a team. And how’d the refs miss it when they were handling the balls in between plays? If the defender spotted it so easily it kind of beggars the imagination that the refs didn’t. Heard an ex-ref on the radio pointing out that the story so far has the refs alerted in the first half, giving them half time to fix it, though we don’t know if they did. But that brings up another question of if they did nothing why? And if they did then the Pats had “proper” balls for the second half when the game turned into a route. There’s a lot to wonder in why the league enforces this rule the way it does.