In a previous life, I worked for a company that manufactures medical exam gloves from a patented (their own patent) artificial latex ("nitrile"). The product packaging labeling used the term "artificial latex" or "nitrile" to indicate that it was not a product made from natural rubber latex.
This was acceptable to the FDA at the time I left the company.
That's where you would venture into the intricacies of clinical evaluation.
Nitrile is a well-known type of rubber (at least today). "Artificial latex" could stand for many things... I never heard that expression before (man-made equivalents of natural latex are commonly referred to as "synthetic latex"). Basically "latex" indirectly comes from the Latin word for milk, and it relates to the nature of the suspension (emulsion) harvested from plants, from which natural rubber is made. So technically the term "latex" could be attached to many things, depending on the creative mind of the user
There is a certain, specific clinical / FDA concern over sensitivity to natural rubber (latex, in lay terms) in some individuals. It has to do with its chemical nature. An "artificial latex" might or might not present similar issues, depending on what its chemical nature actually is. Since it was patented it's hard to say, and I'm not sure how wide an exposure this issue has had at the time. I understand that it was a long time ago, so maybe it even predated FDA's current concerns (which don't go back so far).
Today, a development of this kind would have had to go through some sort of clinical evaluation / investigation (trial) to establish safety, otherwise I assume that a conservative approach would have been followed (i.e. if the chemical nature indicated resemblance to natural rubber, similar restrictions would have been applied). On the other hand, today nitrile rubber gloves are considered "non-latex" gloves so I assume there would have been little concern; regardless, I guess that the FDA would have insisted on the "Not made with..." statement because no one could guarantee that none of the latex antigens are present (albeit in untraceable quantities) and thus its a "better safe than sorry" scenario...