Who checks the game balls?
 

The umpire of the Linesman on the side of the field????? High school

Neither.

The referee approves all game balls.

It is often practice to have the Referee delegate the responsibility to the Umpire. But by rule the Referee is ultimately responsible.

Peace

Canadian Mechanics
 

CANADIAN MECHANICS:

3-man: Referee
4-man: Referee
5-man: Back Umpire
6-man: Back Umpire
7-man: Back Umpire (amateur)
7-man: Field Judge (professional)

In HS games, I farm out the duty to the line judge on my crew. We carry a gauge and a pump.

Last week we were presented balls that had 6.5 pounds of air in them.

Texas: BJ

In Ohio it's the umpire's responsibility.

I mean, is there really any advantage to low air in a football? Why should it matter what footballs are used in the game? I don't think anyone gains an unfair advantage one way or the other but officials do this duty like it is their whole being. Say something about a kid having a back plate or cantilever sticking out and you get the ol' "who really cares, Coach?"

It might allow you to grip the ball better. It can also be a better ball to kick.

Again you are making generalizations, my crew has never really cared or even check the actual inflation other than in college ball where we need to review multiple balls for each team. In HS we get one, maybe two at the most considering we do not use 7 man ball mechanics or switch balls on every possible incompletion. For the most part if we cannot put our thumb totally in the ball, it is likely good. Actually I often think the ball used are at a disadvantage to the team using them as they often are very slick and slippery.

Peace

Yes. There's a reason there's supposed to be 12.5-13.5 pounds of air in a ball.

Yes.

Reduced air pressure in the football increases the coefficient of restitution ("springiness") of the ball (to a point... COR eventually falls dramatically with corresponding reduction in gauge pressure). The specified air pressure (with the prescribed bounds) is defined by the rules committees to provide a consistent game. Allowing a team to put an out-of-spec ball into play can allow the team to kick a ball farther, or cause the ball to bound in a manner that opposing players do not anticipate, which is noticeably different than if the ball were inflated properly.
Other violations you mention, such as players having unauthorized prosthetics, should also not be allowed for different reasons (injury and harm to players, etc.) The fact that an official allowed one form of unauthorized item is immaterial to the fact that use of the other unauthorized item is also an unsporting act. Let's address each issue on its own merits, as neither affects the other.

Um, yeah... I thought you'd played/coached ball. This statement puts that in severe doubt.

Next time you have a practice, get 3 balls, one inflated properly, one under, one over. Kick them. Throw them. Catch them. Throw them at the ground and watch them...

THEN come ask that question again if you need to.

That is a bunch of urban legend and numbskullery! The condition of the footballs is not going to give anyone an advantage.

It's rude not to share when you are drinking.