This is often true, and for thick filleted fish, salmon for example, it allows to remove it quite easily once its side is cooked.
But for some thin fish, it is not always interesting: the skin stretches brutally in contact with the pan, and deforms the fillet into a bow.
This is very pronounced for red mullet, for example. It doesn't change the taste of the fish, but it makes it look a little less appetizing.
But if you start with the flesh side, the skin will not reach the desired crispness, or else with the risk that the fish is a bit overcooked.
What to do?
Try to proceed in 2 times at least: Frying pan quite hot, put your fillet on the flesh side first, let cook 30 seconds, just to seize, turn over (skin side down this time), and cook the necessary time.You will notice at this point that even if the skin is still tense, the flesh, just seized, is much better, and your fillet does not deform, or less.
If necessary (fillet a little thick) finish with a third, short turn, on the flesh side, to finish browning well.
Another possible solution is to scarify the skin side over a few millimetres deep with a small, very sharp knife to prevent it from shrinking.
To sum up: For fine fish fillets whose skin is to be eaten, first cook the flesh side for 30 seconds, then cook the skin side normally.
