But you are still missing it...

The Player may only make the roll for a test when the GM designates that a roll is required... The Player may ASK to make a roll, but the GM is still the final arbiter of whether or not that roll is actually made... if the GM does not agree that a roll is required, then the Player does not get to make that roll...

You can ask all you want, but unless the GM is in agreement, all you will be doing is pestering the GM about making irrelevant rolls...
SO, Unfortunately, the two statements together means exactly that... The Player can only make a test that the GM designates... there are no test made of the players own accord; without the GM's approval, there is no test...

Keep the Faith

No, you are missing it.

The 2 statements together mean that the player can make a test and the GM can ask for one. There can be tests made by the players (without explicit restriction that they cannot do so on their own) and the GM can specify what test he wants when he calls for them.

Regardless of who initiates the request both parties will need to end up in agreement that a dice roll is required. Doesn't matter what's written in the book.

To clarify this point, how about a look at this quote from the same page you two are arguing about

During the course of the game, the gamemaster (GM) will
describe events or situations to you. Using your Character Record
Sheet as a guide, you decide what your character would do in a
given situation. As you roleplay through some situations, the gamemaster
will probably ask you to roll some dice, and the resulting
numbers will represent your character’s attempted action.

According to this, players don't ever roll dice independently, they only roleplay. The only time a player rolls dice is when a GM tells him to, to represent some action he's just performed. In the situation we are describing, by RAW a player would say that he is yelling in a disorienting manner and attempting to sneak past a cop in the middle of the street with no cover. The GM would then decide whether this situation called for an Infltration test, a mix of Infltration and some other test, or no test at all. The player would then roll dice or not depending on the GM's decision and then both of them would determine their further actions based on the results of the GM's decision/possible dice roll. Notably a player may not force a GM to allow him to make a roll, the decision is solely in the GM's hands. Your descriptions of hale-mary chances of success, Toturi, are covered under the rules for longshots in which circumstances that would normally not allow a player to make a test are excused by the player spending Edge and making a lone Edge test in replace of whatever skill he would normally have rolled to represent some extremity of chance that allowed his impossible action to succeed.

This sounds extremely reasonable to me, and uses the rules as written. Can't we just leave it at this?