That entirely oversimplifies things, though. For one, Mozilla owns parts of that third party, therefore they presumably do know what happens with that data and

That entirely oversimplifies things, though. For one, Mozilla owns parts of that third party, therefore they presumably do know what happens with that data and can pull the plug from their side, if nefarious things happen. And secondly, Google can do a lot more with your data than Mozilla and that third party combined could ever do, both from a technical viewpoint in terms of evaluation, linking to other data, distribution, and especially so from a legal viewpoint. Providing this information as you put it would be entirely misleading, even if it is factually accurate in isolation.