As you know, a fake nose is not a nose.
I disagree. You seem to conflate the definitions of "nose" and "genuine nose"; which lies at the basis for your claim, but I'd like to counter that.
Consider this generalized statement:
[adjective] [nouns] are a subset of [nouns], specifically the [nouns] to which "this [noun] is [adjective]" is considered to be a true statement.
Simply put, green balls are balls, furry animals are animals, smart people are people, and fake noses are noses.
I am aware that you can find apparent contradictions such as a "red herring" not necessarily being a herring (i.e. the fish), but that is beside the point. The argument being made by the OP is one of logical definition, not one of occasional homonyms, idioms or figures of speech.
"Fake nose" does not mean "not a nose", it means "not a genuine nose". I suspect you're getting confused because we generally allow the "obvious" adjective to be omitted when it is either commonly inferred or irrelevant for the topic at hand.
Secondly, I want to address the level of scrutiny that you're trying to apply to the language, while at the same time playing fast and loose with questions like:
What do you think?
To which the pedantic answer is "thoughts".
However, I suspect you were relying on the obviously inferred interpretation of you asking us what we think about your interpretation of this phrase, except that you omitted this last part from the question you actually wrote.
Clearly, you allow for shorthand speech when the intended meaning is obviously understood by the listener, since you applied this approach in your own question.
Even though I've already disagreed with your claim that a "fake nose" is not a nose, let's entertain your claim, while also factoring in the permissible shorthand speech that you've used. In this scenario, there are still possible interpretations that are not incorrect in the way you claim that it should be. The first few that come to mind are:
- That nose is artificially created, unlike "real" noses which are organically grown by creatures.
- That nose is a "real" nose, but it was transplanted onto this creature, this specific creature did not grow that specific nose organically.
- That thing we believed to be a nose turns out to not be a nose after all.
With the right surrounding context, "that nose is fake" can be applied to all of these scenarios without being incorrect.