I looked up Epson's website on their DURABright Ultra Ink, which does claim to be pigment-based. You have a valid concern about putting dye-based ink into your printer when Epson uses this special ink. The only thing we can state regarding this issue is that we have been selling this 4-color dye-based ink to our customers for over 3 years and haven't had any major complaints with our customers regarding quality or color.
The main difference between pigment vs dye is that pigment is 'water-proof' when printing on regular copy paper. So if you print using their ink and use a wet hand to wipe across the paper, the ink shouldn't bleed. The opposite would occur when using dye ink. We tested both types of ink on photo paper and both of them don't bleed. We believe this is due to the printing material itself.
Another difference between pigment and dye is that pigment has a more archival quality and last many years. Here is a very useful article that explains the difference between the two inks. http://www.macworld.com/article/54216/2006/12/inktype.html
Once again, a lot of our customers find that dye-based ink suit their printing needs. If you tend to print a lot of photos and would rather use pigment-based ink, we highly recommend to use a 6-color Epson printer. We only carry pigment ink for 6-color Epson printers. If you are hoping just to save money on your every day prints, dye-based ink should be sufficient enough to support your needs.
Hope this helps give you a better explanation and assist you in making a better purchasing decision. Let us know if you have any other questions or concerns!
CisInks Customer Service Team