Hi Confused in KY,
No … this is just marketing terminology which they use because they use latex (which is considered to be “greener” than other foams) and because it may also use a type of polyfoam that uses a chemical derived from soy oil to replace a small part of the petrochemicals in the polyfoam which many manufacturers are promoting as being “green” (and is usually more greenwashing). The description online doesn’t mention this however so it may be just because of the latex or other natural materials in the mattress.
Almost all materials natural or otherwise will produce some type of offgassing so the real issue is the type of offgassing and its “safety”. Safety is always relative to the person (some are much more sensitive than others) but the latex in the mattress (which is most of the foam) has been tested and certified by OekoTex standard 100 class 1 (safe for close contact with babies) and the polyfoam is made in the US which means that it’s probably Certipur certified (you could ask them to make sure but most North American polyfoam is “safe”). Offgassing with these types of materials wouldn’t be an issue for the large majority of people unless they were unusually sensitive and couldn’t be around new polyfoam at all (in cars or furniture etc) which is very uncommon. Memory foam (which isn’t in your mattress) is a more common source of offgassing complaints but even this is usually fine for most people if its CertiPur certified or if it’s made in North America.
There is lots of information and many foundation options in the foundation post here but i would tend to use the one recommended and sold by Denver Mattress as part of the set unless you had a specific reason to use something else.
The specs of the Snowmass and Aspen are sprinkled around the forum in various places but it’s always great to list them again which makes it easier for others to find them in a more recent post on a search … so thank you 
Phoenix