Googlebot snarfing URLs from the ether?

So the other day I had placed a private CGI script on my personal server for testing. (No links to the URL; directory redirects to my home page.) It crashed my server, so I rebooted it and decided to come back later.

Two days later, I get an e-mail from Google's Webmaster tools (which I have configured on that server) that my site is down. Indeed, it needs another reboot, as if someone accessed that private URL. But surely no bot could know that URL exists, right? Checking my server logs I find this (1.2.3.4 is my IP address):

    1.2.3.4 - - [31/May/2013:01:01:41 +0000] "GET /~chris/avcc.cgi HTTP/1.1" 200 283 "-" "Opera/9.80 (X11; Linux x86_64; U; en) Presto/2.10.289 Version/12.02"
    66.249.73.230 - - [31/May/2013:01:02:11 +0000] "GET /robots.txt HTTP/1.1" 200 477 "-" "Mozilla/5.0 (compatible; Googlebot/2.1; +http://www.google.com/bot.html)"
    66.249.73.230 - - [31/May/2013:01:02:11 +0000] "GET /~chris/avcc.cgi HTTP/1.1" 200 291 "-" "Mozilla/5.0 (compatible; Googlebot/2.1; +http://www.google.com/bot.html)"

That is, mere seconds after I had first accessed a URL the world had never seen before, Googlebot decided to crawl my site (as indicated by the robots.txt hit), and then access the URL that was not linked anywhere.

My only explanation is that somewhere between my home computer and my (off-site) server, a Google-affiliated network appliance sniffed my initial GET and sent the URL to Googlebot to be indexed within 30 seconds.

Has anyone else experienced this?

(Yes I know security through obscurity, should use robots.txt, yadda yadda.)