How exactly can you accidentally open bithopper page to internet ? Option for authentication is nice if you do but i doubt its necessary unless bithopper automatically opens port in firewalls and uses upnp.
it cant... however.. a large portion of us, have the port forwarded, so we can check the stats page from anywhere.
second, the newest hopper connects to IRC, and right now they can get your ip from irc.
third the stats page has some sql injection vulnerabilities.
fourth dont worry about it.. it isnt that much of a pain and helps some of our users.