Hi lenyc,
The “fiber” I think you are referring to is called rubberized coir. You can see some comments about it here and here and a forum search on coir (you can just click the link) will bring up more posts that mention it as well. There is also a good article about it here.
You can see some examples of mattresses that use it in post #9 here and a few US manufacturers that use it to a larger or smaller degree include …
http://www.palmpringusa.com/products/
http://www.naturalmatusa.com/prodtype.asp?strParents=104&CAT_ID=162 (for babies and children)
http://www.greenbudsbaby.com/category/cotton-mattresses.html (also crib mattresses)
http://www.savvyrest.com/products/simple-fit-mattresses/simplicity
https://www.flobeds.com/products/organic-mattresses/organic-latex-luxury-performance-mattress.htm
http://www.naturaworld.com/products/organic-crib-mattress/
There is no such thing as a material that is “better for backs”. A mattress that is good for one person’s back may be completely unsuitable for someone else’s back depending on the specific design of the mattress. A mattress that is a good match for you in terms of PPP (Posture and alignment, Pressure relief, and Personal preferences) and keeps you in neutral alignment in all your sleeping positions would be the mattress that is best for YOUR back regardless of the materials that are inside it or whether it would be a suitable choice for anyone else.
Some stores that carry mattresses that use Rubberized Coir in New York that I’m aware of (although there may be others as well) include …
Redirect – Cisco Home (PalmPring)
Organic Mattresses (Coco-Mat and their Greensleep Niu uses coir as well) (NOTE ADDED June, 2016 … they have now closed their business)
Some of the Savvy Rest dealers in your area (they have a retail store finder on their site) may also carry their Simplicity mattress but you would need to call them to find out if it’s one of their models that they carry.
Phoenix