Your website seems to be an aggregator of surface-level news blurbs from the mainstream media and some interviews with individual physicians. There are claims about "made-up" names and "correct scientific names". Putting health claims aside, there are no citations to any legislation that may have prevented a manufacturer from writing these names on a label. This website has a UK perspective, but I was trying to recall if any FDA or FTC regulations would prohibit the coining of new names for ingredients, particularly organisms. I think not.
In biological taxonomy, new names are coined all the time. Aliases for species are quite common. Common names for species are also common. We just learned that a "Buzzard" in the US is different than "Buzzards" in Europe/UK.
Pharmaceutical companies and scientists coin new "fake Latin-sounding" names all the time. So do astronomers! If there can be an asteroid named "25924 Douglasadams" then why can't Activia add a brand-name alias to something they use? Arguably, bacteria replicate so fast that Danone could have a new species if they cultivated it in a lab, rather than in animals.
Conversely, the food industry has taken names such as "milk" and "water", and expanded their definitions far beyond what common people recognize as those substances. Always receiving legal assent to sell fruit juice [nuts are fruits] with a mammalian name.
I've not had much experience with supplements, but more than a few I've purchased made proprietary blends of substances, and named that blend. Totally FDA-compliant.
I think your website got left up because it's fundamentally not a threat to any such practice in labelling.
I hereby address the candida albicans growing in my intestines, to announce that I dub thee candida hackernewsensis because sitting here has undoubtedly helped it grow.