Do people always need skin grafting after fasciotomy surgery?

Not always. Fasciotomy is a procedure to decompress vital tissue that has swollen for some reason and is contained by fascia, the tough unyielding membrane that surrounds muscle. If not decompressed, the muscle (and nerve and tendon and vessels, etc) will die. Sometimes, when the swelling resolves, the fasciotomy wound will close by itself, leaving a linear scar. Other times, skin grafting will be needed.
Not always. There are a variety of methods to avoid or minimize the use of skin grafts for fasciotomy wounds which include specialized tissue expanders or vacuum assisted closure.

Related Questions

Do I need skin grafting after a fasciotomy surgery?

Maybe. If there is a sizeable open wound that would be too large to be expected to heal on its own, then it may likely need skin grafting. Depends on the amount of local swelling, signs of infection or not, and how healthy the tissues are in the area.
Possibly. It depends on big it is. Usually fasciotomy sites heal quickly enough that skin grafts are not necessary. If it is large, then skin grafting might make it heal a little faster.