Worked in equipment for a while and I know how to fit a helmet. Never did I call out any equipment managers. A certified person fitting a helmet can give a player a great fitting helmet, and if the player doesn't buckle it up it can definitely come off.
Helmets lose a little air over time and if the player never says anything about it, it's not likely the equipment person will catch it unless it's very loose, especially with 120+ players to watch. They aren't re-fit every week. Players with a good fit -- and this isn't a rule, just an observation -- take off their helmet and have faint indentations in their hair or a red spot on their forehead in the shape of the interior pads. Some helmets do fit around dreadlocks better, or around heads with a more/less pronounced occipital or frontal bone.
I cringe when I watch high school and lower football games and see helmets rattling around, or hear of players personally shaving down pads inside of helmets because it was all that was left but was too small for them.