>>141
In general, 全然 is used as a short one word reply only when standard grammar and word usages can determine the omitted part.
For example, if you're asked "何か問題がありますか。 (Is there any problem?)" and you say "全然。", then you always mean "全然問題ありません。 (Not at all.)" because "全然問題あります。" doesn't make sense in the standard Japanese language. Certainly native speakers sometimes say "全然問題あります。", meaning "There IS a problem" in an informal conversation, but this possibility is ruled out when you just answer "全然。" because it is not a standard usage.
By the same token, when you're asked "どう思いますか。 (What do you think of this?)," you never say "全然。" because no standard grammar or usages can tell what you mean.
As for the connotations of 全然, there is much more than what she said (I'd say she is wrong). Roughly speaking, it was either positive or negative until about 50 years ago, then it lost certain usages (still could be used in a positive sense in a restricted way). But recently the lost affirmative usages revived, especially among young generations, in a slightly different way as in 50 years ago.
For instance, "全然間違っていない (It is absolutely correct)." has a positive meaning but this has long been accepted as a standard usage. "全然おいしい" is an example of the revived usages. This was not strange or anything and meant "delicious," but strict grammar of contemporary Japanese forbids to use 全然 without ない. But now it is acceptable as an informal usage and means "Yummy!"