I think that I asked something very similar to this before, but consider this sentence:
I do this all the time on Facebook, and I’ll never convert hardcore conspiracy theorists, but I can actually reach a large number of people who are in the middle and who are just curious about what people are talking about.
So it has the following structure:
X, and Y, but Z.
Does the "but" attach only to Y? Or to X? Or to X and Y?
Not sure if this is the ONLY ambiguity...there may be more ambiguities in that structure too; is this the ONLY ambiguity in that structure?