PT is done in shorts and a short sleeve T shirt during the summer, so tattoos on the lower legs or forearms can't be covered up. Often times PT is done on bases on foreign soil, where troops from other nations are directly interacting with our troops, along with civilians and whoever else may be around.
Something else to keep in mind is when you sign up for the military, you no longer have the right to make your own choices. You become property of the US Gov, and you do as they say.