I don't think it really is in the circumstances we contemplate this threat in. In both the search engine case and the ChatGPT case, we're talking about circumstantial evidence (which, to be clear: is real and legally weighty in the US) --- particularly in the CBP setting that keeps coming up here, a Border Agent doesn't need the additional ChatGPT context you're talking about to draw an adverse conclusion!
I think at this point the fulcrum of the point I'm making is that people might be inadvertently lulling themselves into thinking they're revealing meaningfully less about themselves to Google than to ChatGPT. My claim would be that if there's a difference, it's not clear to me it's a material one.
Ah. Yeah you're more boned if you confess to ChatGPT that you've killed your wife than if you just googled for how to bury a body, but at the edges where people are using ChatGPT as a therapist and someone disappears, and the person who did it is smart enough to use incognito mode to search how to bury a body so it doesn't show up in court, how everyone feels about the deceased is gonna get looked at, including ChatGPT conversations. That's new.
I think at this point the fulcrum of the point I'm making is that people might be inadvertently lulling themselves into thinking they're revealing meaningfully less about themselves to Google than to ChatGPT. My claim would be that if there's a difference, it's not clear to me it's a material one.