Let's step away from the Bills and see what "control of the 53 man roster" means in real life for other teams.
Here are similar Browns mentions of control of 53 man roster for the GM and game day roster by the coach.
Haslam promoted Farmer from assistant general manager to GM. Farmer immediately took control of the team’s football operations and will have final say on its 53-man roster. New coach Mike Pettine will have final say on the 46-man, game-day roster, Haslam said.
http://www.ohio.com/sports/browns/new-browns-gm-ray-farmer-has-control-of-53-man-roster-will-report-directly-to-owner-jimmy-haslam-in-aftermath-of-stunning-shakeup-1.465923
Ok, so far so good.
Now let's see how Farmer's "control of the 53 man roster" worked in the draft room in 2014.
Homeless man convinces Browns owner to draft Johnny Football!