The virus scanner inside Google Chrome, you're mentioning, seems to be somehow connected with Settings > Advanced > Reset and clean up. So, this process may not be that unknown, as you initially said. But, true, you're right that Chrome wants to be much more than just a web browser.
The problem described in this thread is directly connected with the problem described here:
https://superuser.com/q/697618/156554. This is because mentioned error screen about incompatibility between TortoiseSVN and Google Chrome appears only when "Google Chrome didn't shut down correctly" error appears first.
When browser is launched correctly and you manually go to Settings > Advanced > Reset and clean up > Update or remove incompatible applications then you can clearly see that there are no problem and "Done! No incompatible applications found" message appears.
Thus this is 99,99% a bug in Google Chrome that has nothing to do with TSVN except for calling its name.
The good question is whether to bring this bug to Google Chrome's bug center to "clean up" good name of TSVN or whether it is better to ignore it, since it doesn't actually corresponds to TSVN?