The signalling fallacy that seems to get all the attention is what I call a fallacy of signalling "implication", i.e. when someone says:
"Justin Bieber's music is crappy"
The rational implication of this communication is that Justin Bieber's music is, in fact, crappy according to some standard. But if what they were actually implying is that they don't like Justin Bieber or that they are signalling a tribal affiliation with fellow JB haters, then they are committing a fallacy of signalling implication.
But that's not the only type of signalling fallacy. You can also commit a fallacy of signalling "inference", i.e. consider someone who says:
"Atlas Shrugged is the greatest book ever written".
Again the rational implication of this communication is that Atlas Shrugged is, in fact, the greatest according to some standard. And if that's what they were actually implying, but then you infer that they simply enjoyed the book a lot or are signalling a tribal affiliation with fellow AS lovers, then you are committing a fallacy of signalling inference. (Note that this goes the other way, too. If they *were* implying simply that they enjoyed the book or were affiliating themselves with a tribe and you inferred they were making some factual claim, that would be just as wrong).
So it's important to be aware of two sides of this fallacy. If you happen to be overly concerned with the former, you might fall victim to the latter.
I basically agree with Luke_A_Somers. I would suggest not changing examples. They are both of the form "X is Y." Just use one so it is easier to see what distinguishes "implication" from "inference."
Also, it needs to be more clearly stated that the implication fallacy is on the side of the person making the statement while the inference fallacy is on the person interpreting the statement.
This actually seems like a good example of both parties committing their respective errors. Consider stating that directly.