Marketers make false claims intending to deceive their customers all the time, which they probably dress up as hyperbole. However they usually back their claims with logic/reasoning and not with quantitative results. Is it hyperbole if they actually believe their claim? How would you even go about proving a claim like this one. I know they manage to convince many of their customers of this.

Since subjectivity can't be proven and there isn't such thing as the "truth," does the "truth" or verdict just come down to what one judge and jury determines?

You are correct. The judge will know "mere puffery" when the judge sees it, and may just throw out the case. Freedom of speech versus commercial speech.