I'm not a conspiracy theory kind of guy so I believe Apple simply didn't say it because it can't. We don't even know the method of the guy's "public" Wi-Fi sign-in, or how it was set up like you said. The way I see it is simple: iOS 9 can't automatically sign-in this kind of Wi-Fi that need signing-in on browser. it doesn't have this ability, and so doesn't the watch.
If
@frumpy16's watch DID connect then his phone didn't need to sign in on the browser either. And if that's the case then of course his watch will connect but that's not what we're talking about here. This thread isn't for "can my watch connect while away from phone?" since we already know from beginning that it can.
If he can shoot a short video showing us he has to log in to this Wi-Fi on browser then turn on Airplane mode on his phone. And show us the watch can still get notification THEN we will have concrete informations to rely upon.