I've been following this post for the past couple days and decided to contribute my 2 cents worth--like my daughter says, "opinions are like ....", anyway. It seems that any material that can be applied to the back of a bow and prevent or lessen the likelihood of the bow's exploding is good. I agree with PatM that it would take 2 or 3 layers of linen to equal the depth/mass of another material such as rawhide, goat skin or sinew. That's one reason I can't buy into the argument that multiple layers of linen serve no purpose. While doing so will add weight, it still won't be any heavier than a leather backing.
And to say that with time Titebond ( I've never tried TBIII) will dry and get brittle just isn't true. I have a partially full quart bottle of TBII with dried glue in the nozzle and around the cap. Every now and then I have to remove it to keep the glue flowing, yet its still flexible and pliable.
I don't have a degree in engineering, but it seems that part of the strength of a material is its cross pattern or perpendicular weave. While sinew will stretch and retract linearly like a rubber band, the cross design in woven material would lend additional support to a linear grain, especially in woods that aren't interlocking grain like elm or hackberry are. For example the heavy leather wrapping found on the Meare Heath bow which also gave evidence of having been drastically, if not purposely, grain violated on its back.
Regardless, I've heard that cracking sound before, and in one instance wanted to believe that it had somehow come from the tillering tree, so I continued to shoot this cracked linen backed hickory short bow for several days until the limb was bending so far and so easily that the break could no longer be ignored. The bow never exploded, maybe because of the cloth backing...who knows. Just my 2 cents.