These rumours have been flying around for years, but I have never found them very convincing, or seen good evidence.
In fact the new elders book gives this instruction:
LIBRARY
39. Each Kingdom Hall auditorium should have space for a library. (od p. 61 par. 19) The library should contain publications for each language group using the auditorium. The bodies of elders should determine whether the library will provide publications in printed form, electronic form, or both. Since some publishers and inter- ested persons do not use computers or electronic devices, the elders should give careful consideration to the needs of such in- dividuals when making decisions as to the Kingdom Hall library, especially before deciding to eliminate printed publications. If the publications will be provided in electronic form, such as on a de- vice or on a computer, a printer should be made available. At least one responsible brother should be assigned to keep the li- brary up-to-date and in good order.
40. In the event that the bodies of elders decide to eliminate printed publications from the library, care should be taken not to discard items that have historical significance. The branch office may wish to add such items to its library or to its archive of historical ma- terials.
An interesting exception appeared in a recent elders letter which states that an old brochure aimed at Muslims is to be specifically discarded. Elders are also instructed to destroy old manuals and other policy documents so they don’t get mixed up with new ones.
There has never been a general instruction to destroy old literature as far as I am aware. Local elders dumping old literature off their own back I can imagine happens from time to time. In fact the instruction in the elders book that “care should be taken” is pretty good evidence that elders are sometimes careless in what they throw away.