In FPS games, EVERY player needs to be able to stand up and make a difference. In a small squad-based FPS (your example NOT being one of these, where Brink is), that means balance needs to be retained between individuals in a 1vs1 encounter as well as the large-scale "big picture" balance of the interaction of different elements.
That's actually very much part of what he's trying to saying. But it's about the game balancing out the game mechanics, not balancing out player ability which seems to be the counter.
The game manufacturer should balance the weapons within their sets -- all ARs should add up to the same grade, but Rifle A should work better in situation A and B should work better in Situation B, whether it be DMG/ROF/ACC that makes the difference.
They should balance each Weapon set further by situation -- Shotguns should have serious ability and power at close range and should be able to beat (assuming equally skilled players) rifles within that range. Having an outlier (a shotgun with better range or a rifle that works better in close) is fine, but on the whole weapons are chosen for situation.
They also need to balance abilities (my heal vs. your turret build) and maps (have the areas and required movements to force all different weapon usage).
It is then the player's responsibility to bring their skills and understanding to the game to give themselves the edge with their choice of "balanced" gear.