You elided the word "Empirical". Say his wife made it empirically as water-tight as she can: for instance she hires a PI who follows him 24/7. The PI finds nothing out of the ordinary. How is this even still cheating?

Maybe he was cheating before or after, sure, but not during. No court would buy that.

...At least, that's how I interpret 'empirical consequence' - something observable or detectable, at very least in principle. Do you mean something different?

(Right this minute I'm coming from an empiricist framework where acts require consequences. If you're approaching this from a realist or rationalist view -which I suspect-, I'd be interested to hear it!)

@Kim_Bruning The point of the experiment is that there is some opaque boundary where the behavior is indistinguishable--that's the empirical stance of behaviorists, what goes on inside "doesn't matter." The empirical boundary of a husband and wife might be home life and time together. If you "pierce" the Chinese Room, you see a guy with an exotic setup. If you pierce a native speaker, you see a brain that electrochemical that has microtubules that collapse the wave function (or whatever), just like YOU have, and YOU know you understand (at least relative to English)...these are VERY different things even if they are, externally, yielding the same behavior. So yes, you could hire a private detective and so-on, but the whole point of the "empirically indistinguishable" is that it is empirically indistinguishable relative to some boundary (hence, room). If the Chinese Room was TRULY empirically indistinguishable, then inside it would be a human producing Chinese, not a non-native speaker and a program.

btw--if you'd like to keep the conversation going, email is on my personal webpage in my bio.