I sincerely doubt it has anything to do with a whitelist of user agents. It is probably triggered by a failure to evaluate the botguard program, which indicates that your browser may be under the control of malware.
If your browser's user agent lies outside the "supported" list, you will be presented with a page telling you that your browser is insecure. It's a whitelist. I... Am unsure why you think this is not the case.
You can test it. Or look at any of the many articles after Google made the change.
A freshly installed Firefox, with a useragent of "Bob Dobbs 42.69" yields the "Your browser may not be secure" page, for myself. Both within and without a VM.
So, yes, I think I'm speaking to what the thread is actually about.