Not sure if he has authority. Not all time. Yes for a small company he did. For a large company I discuss it with him because he is the one who knows what I did last year best. If I got to higher ups and say "give me more money", they'll say something like "I think I've seen you in the kitchen, or the conference room". Well, in reality they'll read a performance review probably from my manager. And then probably talk to the manager anyway...
But what happens is I talk to my manager and they they'll go find out and make a case for me if they are not authorized to do it themselves.
> If he is then, again, there shouldn't be a problem since you both agreed that your compensation is fair for both sides.
Well that was the original premise of the post. If negotiating like one negotiates buying a car, showing counter offers and so on. They might feel like you tricked them, if you then don't do the job to the level of your salary.