I can confirm that copying of secret books appears to be going on. I had a slab containing the secrets of fire that was learned from a few times and then lost in a seige around the year 60. However, in Legends Viewer, people continued to learn the secret of fire from it even after it was "lost". This seems to indicate copies were made, I think?
More scientific results: secret learning may affect the outcome of wars in worldgen. I have a tribal frogman civ that was having trouble surviving until I added secrets for their forced religious spheres of water, moon, and nature. Post-secret addition, the numbers of frogmen surviving worldgen has gone up noticeably.
Another scientific result: creatures that learn a secret, then become a vampire apparently lose their knowledge of secrets, or else vampirism interferes with displaying it in Legends Viewer.
I'm doing some more tests to figure out how secrets are generated and assigned. I turned up the number of secrets to 1000 on a large world to see how much I could make them proliferate; a fair number of non-necromancy secrets spawned and spread, but looking at death-sphere deities in Legends Viewer, they appear to be associated with 1000 necromancy secrets! I'm clueless how the secrets I made fit into this number. Based on the suggestions of other people here, I added duplicate secrets with the same effect for fire, volcanoes, sun etc. I'll see how this plays out.