I'm sorry to say that this isn't true. There are absolutely solvents in eco-sol inks and they cause cancer and birth defects. After the ink is dry I believe everything you said is true but when it's a liquid, and also breathing in it's vapors, it absolutely is hazardous to your health.
They do have solvents. But they are not hazardous in typical workplace exposure, which means the vapor that enters the room air during normal use. Here's a cut and paste from the MSDS for Epson Ultrachrome GS3 ink:
"
Safety Data Sheet
HMIS rating:
3. COMPOSITION/INFORMATION ON INGREDIENTS
Substances
N.A.
Mixtures
Hazardous components within the meaning of 29 CFR 1910.1200 and related classification:
65% ~ 80% 1-ethoxy
-2-(2-
methoxyethoxy)ethane
CAS: 1002-67-1, EC: 213-690-5
B.6/4 Flam. Liq. 4 H227
10% ~ 12.5% gamma-Butyrolactone
CAS: 96-48-0, EC: 202-509-5
The product is not classified as dangerous according to OSHA Hazard Communication
Standard (29 CFR 1910.1200).
5% ~ 7% (2-Methoxymethylethoxy)propanol
CAS: 34590-94-8
The product is not classified as dangerous according to OSHA Hazard Communication
Standard (29 CFR 1910.1200).
1% ~ 3% Carbon black
CAS: 1333-86-4, EC: 215-609-9
The product is not classified as dangerous according to OSHA Hazard Communication
Standard (29 CFR 1910.1200)."
So one is listed as flammable. The others are listed as not dangerous according to OSHA Hazard Communication Standard.
Now, there are indeed people who believe that there is no safe level of any chemical, and so on, but if we work that way, we would never paint or print anything.