How could publishers, in particular disreputable ones, prove that you “signed” a copyright agreement?
First, I would like to clear up a little misconception. A signature is never proof of anything. There is very little difference among a hand written signature, pressing the I agree button, and writing an 'X' on the signature line. They all carry the exact same legal weight provided they were done in a proper fashion. The only time a signature is ever really sufficient proof is when it has been notarized (which is much more than just the notary's signature). So, signing a paper and faxing it over, for instance, doesn't have much more value then pressing your "I agree" button. Without being notarized, signatures in any form are simply evidence. 

Third parties, in this case, can effectively act as notaries to a certain extent. There tend to be very strict guidelines when dealing with electronic signatures. Depending on the field and the government involved, how the signatures are stored is often very important. Other than the legal requirements, the person or court would need to ask the question "Why would the third party forge the signature" and "Was the signer who they say they were". Usually these are emailed and involve a unique token, so identity is based on the security of email and the token is stored and hopefully not accessed. Periodic backups (using non-re-writable media) that are stored securely can often be used to ensure data hadn't been added or modified. 

It is nearly impossible for a party of the deal to serve as the sole witness to the authenticity of any signature as they generally have reason to lie. Instead, they need to show that you agreed to transfer copyright as evidence that the signature is authentic. If they don't have you agreeing to the publication somewhere, then they are just waving around a piece of paper with an 'X' on it.