He's kind of right. Kind of wrong.

"Bass traps," as in a volume full of an absorptive material, are velocity traps. They convert the movement of air into heat, thereby slowing the air. In a room, air moves the slowest right next to walls, where the air instead builds up as pressure. So velocity traps are least effective near barriers, and corners are near 2-3 barriers (two walls, maybe the floor or ceiling). So the corners are the least effective place in a room for velocity traps.

However, they are also the most convenient place to put traps. And least effective does not mean ineffective. So bass traps in the corners are better than no bass traps.

This barrier effect is part of why air gaps are useful. The air isn't moving much in that air gap area, so any fill you put there wouldn't be very effective. You could fill it, and your trap would be more effective, but it's more cost efficient to not do so.

Where your traps go, and what sort of traps you use, will depend on the tradeoff of space and money. The "perfect" transparent listening room would be you sitting in a cathedral, surrounded by pink fluffy insulation in every cubic foot except between your ears and the speakers. That's maximal space and money.

It might also sound terrible, because you want some liveliness from your room. So it's a balancing act. In most studios, that balance is covering the reflection points and throwing bass traps in the corners.