The "You are/are not" message seems to be included in the page source before any Javascript runs. Is it possible there are detectable differences in the original HTTP request itself?
My guess is he's looking at XSS mitigations or similar that aren't in headless?
If it were doing something like using CSS being non-blocking (? I don't know that it is) that's a server side detection .. but that would seem to work even against spoofing.
But he says if you spoof another Chrome-based browser (Safari) he can't tell. So he's looking first at UA?? That's weird.