Trouble ないで vs なくて


In this [answer](https://japanese.stackexchange.com/a/5926/32056) it is said
that the usage of なくて is narrower than ないで(ないで can always replace なくて
according to the logic explained and is ambiguous because of that)

But in this [question](https://japanese.stackexchange.com/questions/63175/why-
is-it-%E3%81%AA%E3%81%8F%E3%81%A6-and-not-%E3%81%AA%E3%81%84%E3%81%A7), the
answer says that ないで cannot replace なくて in the sentence discussed.

What is the reason behind that?

