"Who wouldn't trust "an IP address scrawled on a piece of paper" ?"
Apparently not most of the people who actually use one of those watches, which I guess is not an insignificant number of people. (Though who knows how many buy them, see the scrawled URL and immediately return/bin the watch).
I'd be extremely dubious about downloading an app that could only be acquired from a URL and not via any of the major Android appstores, especially if said URL did not belong to a major known company.
I wouldn't even consider one that gave a URL in the form of an IP address rather than an actual domain name.