If the intuition you're referring to is the idea of finding a self-adjoint operator with eigenvalues exactly corresponding to the nontrivial zeroes, then yes. T

If the intuition you're referring to is the idea of finding a self-adjoint operator with eigenvalues exactly corresponding to the nontrivial zeroes, then yes. The existence of such an operator would guarantee that the zeroes are all on the critical line. If you're referring to the heuristic arguments for why their proposed not-quite-self-adjoint operator should have only real eigenvalues, then no.