[gaovvpzq] RH but not GRH

Create a proof of the Riemann Hypothesis that cannot be generalized to the Generalized Riemann Hypothesis.

This would be a good act of trolling by a superintelligent entity (assuming RH is true).

What is the theory of "proof that can or cannot be generalized"?  Is it possible no such proof exists (assuming GRH true and provable); that is, every proof of RH can be generalized to GRH (assuming GRH is true)?  Can we get into such a situation even if RH is not equivalent to GRH?