Could Riemann hypothesis solve certainly RSA?
It's not that proving the Riemann Hypothesis would itself lead to a breakthrough against RSA.  Rather, it's speculation that the methods leading to the discovery of a proof of the Riemann Hypothesis could lead to a profound discovery about prime numbers that, say, makes factoring easy.

The reason that proving the Riemann Hypothesis in itself has no bearing on RSA's security is that we can simply accept it as true now.  We don't need to wait for a proof to use the Riemann Hypothesis to find holes in RSA.  If we found a way to use the (apparent) fact that all nontrivial zeros of the zeta function have real part $\frac 12$ to crack RSA, and this crack actually worked, then it simply doesn't matter whether the Riemann Hypothesis was proved.