Metal Gear Solid V is set in 1984. Most '80s action heroes wore more cloth on their foreheads and biceps than Quiet does on her entire body.
Creator Hideo Kojima crowed that her costume's explanation was so good it would make people feel bad about mocking him.
Translation: "I'll show you. I'll SHOW YOU ALL (her tits)."
The explanation? Quiet was burned almost to death. Great start! She only survived thanks to parasites making her photosynthesize and breathe through her skin. She must remain nearly naked at all times, or she'll suffocate. And if she ever speaks English, the parasites will start multiplying to kill her and every other English speaker in the world.
Why That's Bullshit:
She can totally wear clothes.
"What, this old thing?"