I feel like you're fighting the hypothetical a bit here.
Perhaps "cat" was a bad idea: we know too much about cats. Pick something where there are some properties that we don't know about yet; then consider the situation where they are as the actually are, and where they're different. The two would be indistinguishable to us, but that doesn't mean that no experiment could ever tell them apart. See also asparisi's comment.
I am most assuredly fighting the hypothetical (I'm familiar with and disagree with that link). As far as I can tell, that's what Thagard is doing too.
I'm reminded of a rebuttal to that post, about how hypotheticals are used as a trap. Putnam intentionally chose to create a scientifically incoherent world. He could have chosen a jar of acid instead of an incoherent twin-earth, but he didn't. He wanted the sort of confusion that could only come from an incoherent universe (luke links that in his quote).
I think that's Thagard's point. As he notes: these ...
Thagard (2012) contains a nicely compact passage on thought experiments: