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The way the script is setup is when someone clicks on that button, another script is called to log the "click" in our database, then the script redirects the browser to the third-party site.
I'd second g1smd that this is quite improbable for the action-target-CGIs of POST forms. However, Receptional Andy in the above thread assumes some glitch in parts google's infrastructure as one possible cause for the mysterious behaviour in the crawl process. So you'll never know...
But may I raise a more serious question: If you are so unsure about this relatively basic knowledge on CGIs: Are you sure your script is hacker safe? Have you ever heard of mysql-injection-attacks and what did you undertake to protect against them?