1script - 9:49 pm on Sep 3, 2011 (gmt 0)
Tried both Yahoo and Bing - no links between those sites are found.
Have you used other backlink checkers like Yahoo Site Explorer to see if they show these links?
I mean, both Site A and Site B have a register.php URL. Since they are based on the same software and somewhat similar (but not same) template, the register.php pages might look somewhat similar (though graphics are different) and the HTML code is somewhat similar, but that shouldn't really matter to a bot since in the end they are not 100% same.
I also thought that I might be accidentally loading Site A's Google Analytics code into Site B but upon closer review that is not the case. Some sites had GA but some didn't.
I've also done extensive testing of Site B's register.php script trying to feed it all sorts of weird variables to make it redirect to Site A. However, the script does not accept GET queries and register_globals is off on this server, so in order to mess with the script (even though I could not find a way to "create" a link between the sites by messing with the script) Googlebot should actually make a POST query, and I don't know if they can (or even should) do that.
One other thing: Site A and Site B are hosted on different servers, completely different IPs.
So, in the end, I'm left with a conclusion that Google makes determination about the link between the two sites (not just one singular link: one of these A-B pairs shows 200,000+ links!) based on superficial resemblance of ONE particular URL on these sites. How crazy is that?!