J wrote:

The library at school has several instructional audio cassettes they
lend out. Several of these tapes have become somewhat garbled, fading
in and out and echo-ing.

The above is a good clue to what happened. Echoing equals print through.
That's when there is a transfer of information from one layer of tape to
another. There is no recovery from this. Prevention requires the tape be
left in a "loosely" wound condition. For most tape machines, never
rewind a tape until needed as fast winding gives a tighter wrap.

The library staff claims that this is
because someone has attempted to copy the cassettes. I say this is
hogwash, as I am unaware of any schemes for copy-protecting audio
cassettes -especially that would destroy the source recording! I'm an
electrical engineer and a recording hobbyist. Am I simply ignorant of
the methods? If I'm right, what is the most likely explanation for
this type of damage? Heat? Magnetic destruction? Wear?

You are correct, hogwash.