One of the main components that has a large effect on this, I assume from my own observations, is that they may have the smaller tanks (50 gallon or smaller) plumbed together into a much larger system which alleviates water quality issues at individual level.
The LFS near me has imported purple tangs 3-5" long recovering from HLLE in compartmented acrylic tanks where each compartment is smaller than a 5-gallon tank. The compartments have slots in the side so all water is shared in a large system and also plumbed together through a large sump with huge skimmers and such for efficient nutrient export.
The equipment is usually remote from the actual systems and may not be seen by the customer.
I also think, as others have mentioned, that they rely on the fish being confined short-term and selling and replacing often enough to not lose as many fish due to stress.
I don't think it would be a good idea to overcrowd a single tank. See above about common-plumbed large systems.