You are absolutely right. These days a lot of people use the word "全然" to mean "completely" as in "It's completely OK." But actually, "全然" is more like "at all" in the phrase "not __ at all" like "It's no trouble at all" which will be "全然問題ありません。" And as for "全然大丈夫じゃないです" (or 全然大丈夫ではありません), this sentence is grammatically correct. But "全然ダメです" is, although a lot of people say it, grammatically incorrect. But similar phenomenons happen in other languages, right? For example, the expression "close proximity" is actually incorrect because the word "close" and the word "proximity" both mean "nearness" People also say "I could care less." instead of "I couldn't care less." But in any case, your Japanese is correct. I hope this helps.

You've already got the answer by yourself. It's the question of 全然 in a positive/negative sentence. FYI you might have Japanese sense because 全然 used to appear only in negaitive sentences. I think it has been accepted in positive sentences as well just for 30 years.