Interesting idea, I'm not so sure I agree about "For the more gung-ho, obfuscate the URL and use SSL (e.g. https://yoursite.tld/something-unguessable/monitors.txt) and tell your provider where to find your monitors.txt'.
If "something unguessable" is a 64 bit number from /dev/random, and it's disclosed only to monitoring providers, and indexes are turned off on the server, it's not "security through obscurity"; it's a key.
Virtually every web app in the world relies on a similar security system. You just don't notice, because we call the "key" in those systems a "cookie", not a "dynamic URL path component".
There are reasons why the URL key is inferior to other keys used by web applications, but they are fiddley. If monitors are unlikely to have extremely sensitive information in them (and you'd hope they wouldn't given their intent), it's fine to use URL keys.
http://en.wikipedia.org/wiki/Security_through_obscurity