The rules seem to state that the ref is the soul judge of determining if a football complies with regulations. It doesn't specify anything about what happens in the event where they were wrong about an initial judgement if a team intentionally provided balls they knew shouldnt pass inspection.
Furthermore, as others have pointed out with specific quotes from the rulebook, there are enough broad rules about team and organizational behavior and not ruining the integrity of the game that very well could apply to this scenario and justify punishment.
Conduct and unfair action rules are entirely subjective, and to my mind having the referee check an underinflated ball or using any ball approved for use by a referee is not unfair. Again in my opinion the Patriots will not be punished if it turns out this is what happened.
Can you find a rule that states it is illegal to play with an underinflated ball?
You still have not answered why the other rules cited do not apply. I specifically cited Rule 17, Section 2, Article 3, Rule 17, Section 2, Article 1, and the Code of Conduct, for instance.
Because if that is what occurred what they did is not unfair.