If it can be statistically proven that this is occurring more on Firefox than Chrome then Google has a really, really big problem. The burden to make sure it isn’t is on them, most especially in the EU. Google is facing a very real future where they will have no web browser and possibly no operating system.
It absolutely is happening more on Firefox. I open Chrome almost exclusively to bypass CAPTCHAS, and I doubt they will get in trouble because Chrome gives more detailed data due to its invasive lack of privacy. You can't really blame Google for using its own tech to provide "better" results, but it is high time we started blaming them for the massive privacy violations they use to make their convenience work.