Your credit score is maintained by a bunch of goons in a protection racket. 'Shame if anything would happen to that fine credit score, let me 'protect' it for you".
Unfortunately, there are few legal standards in this area. Any business can report that you have not paid something.
Write a letter to google's corporate address with all your evidence, enclose a literal paper check, keep a copy of everything. Point out in your cover letter that you are discharging your responsibilities especially regarding collections, and collections will be considered an illegal action. If it comes back and harms you, you have cause of action and documentation. Take whatever action is appropriate for harm (apparently arbitration can be really good for small cases like this, less hurdles, more getting the companies money).
And just don't get bent about it.