The idea of "bideniability" is defined early in the paper as meaning that there is no way for an adversary to distinguish between real and fake (key, randomness

The idea of "bideniability" is defined early in the paper as meaning that there is no way for an adversary to distinguish between real and fake (key, randomness, message) sets, even when they receive one of those from both the sender and the receiver. So, by that definition, no plaintext can be proven to be fake in a bideniable system. It doesn't matter whether sender and receiver both lie, or whether only one of them does. I haven't read far enough to be able to answer the first part of your question (does faking require access to the real ciphertext) but based on the symmetry of the definition of bideniability, that would be surprising.