Bardzo dobre pytanie. Nie mam pojęcia jak na nie odpowiedzieć. Absolutnie, nie mam pojęcia.
On one hand, I've read several comments by linguists saying that both "niczego" and "nic" are perfectly fine Genitive variants, as long as it's dependend on the verb and not the preposition. So in theory, this should be fine. But it just sounds so totally wrong to me... so wrong. Although technically, it seems that it's fine...
"Nie potrzebuję nic" sounds kinda weird to my ear, but only kinda, especially compared with "Nie boję się nic". And I would be okay with "Nic nie potrzebuję", actually.
Another Polish person said the same thing. He said both genitive forms are possible for negative statements such as these sentences; however, genitive case with a preposition MUST use the niczego (np. Bez niczego a nie bez nic).
Interesting Note: In Russian, you can only say ничего (the Russian "niczego"). Нчито is actually not very often seen.
Isn't "scared of" and "afraid of" the same in this sentence? Both should ideally be allowed.