The sentence you quoted says the manager “wouldn’t, or shouldn’t” hire these candidates. In my understanding, this means they aren’t needed, not that they aren’t qualified. That’s the essence of the “hire to fire” practice - hiring someone not because you need them to do the job, but because you need to meet your firing quota.

For a person to get placed on a team at Amazon, the manager must be making some representation that they need another employee. Amazon isn’t going to waste headcount by giving it to managers who don’t ask for it. This means managers have control over whether hires are joining their team. Therefore a manager can execute the plan of hiring to fire. It doesn’t matter whether they have the power to approve a specific candidate.