Old roofing felts "ARE" recyclable (as are shingles), here in most New England states. As a matter of fact if one bids on many local (public) town, state or federal reroofing jobs these days there's a very good chance that recycling roofing waste products will be written into the contract documents. Call you local waste management companies & ask them about their recycling program for roofing materails.

There is a difference between coal tap "pitch paper" & asphalt paper. Both are still recyclable. Coal tar picth is shing & flaky not like a "rag" or fiberglass felt paper & also it smells acidic. By the 80's asbestos paper was not being used any more within the industry.
If it's rotted & not a breathable it is most likely a "rag" felt paper & not of fiberglass, still it is asphalt impregnated.

There is no "salvage value" to the contractor (only when there are resalable metals like copper of aluminum, not roofing products). In the New England area the disposal companies will tell the contractor what's acceptable for waste their various containers.
Recycle materials will go in one container, landfill materials in another & hazardous waste will be handle in another in various ways, contained, wetted down, double wrapped in closed plastic containers before going into special dumpsters & those dumpsters are also treated in various ways before ending up in a credited or licensed fill.
The contractor has to abide by the local waste industries, they will not except construction material without conforming to what the local standards are & tracking waste is fast becoming part of the business.
When I see bids going these days out many of them now require a waste disposal plan prior to the bid awarded
   
Barry