Poor quality glue usually means that it has lost some or all of its ability to hold things together. Poor quality glue might lead to a sinew backing peeling off from the wood over a short period of time, for instance. Also, the thicker the sinew job, the higher the quality of glue you need.
A thin backing can be held on effectively with just about any type or grade of animal glue. That goes for sinew wraps as well.
Knox is actually pretty good stuff. As a general rule, if it smells bad, it's not good.