From your mistyping an "r" as a "к", I am guessing you're Russian. That, in turn, suggests to me that the people criticizing your work are likely to be Russians as well.
Russian uses double negation. As indeed do certain varieties of English. But Standard English does not. Your critics are not aware of this simple fact, and instead are simply translating from Russian word-for-word.
Observe:
Девушка никого не встретила.
Standard English: "The girl didn't meet anyone".
Literal translation, not Standard English: "The girl didn't meet nobody".
Я ничего не знаю.
Standard English: "I don't know anything".
Literal translation, not Standard English: "I don't know nothing".
Никогда тебя не забуду.
Standard English: "I will never forget you".
Literal translation, not Standard English: "I will never not forget you".
Никогда никому ничего не скажу.
Standard English: "I will never say anything to anyone".
Literal translation, not Standard English: "I will never not say nothing to nobody".
You get the point.
In brief, you are correct, and your critics are wrong.
You might wish to inform them that when writing in English, we generally tend to apply the rules of the English grammar, and not those of Russian.