Design against buckling of thin shells at high temperatures often follows the code RCC-MR. RCC-MR allows three methods to quantify shell imperfections for use in safe load calculations, where lower imperfection values raise the safe load estimates. In recent work, we showed that the third of these methods can sometimes yield remarkably low imperfection values, leading to potentially nonconservative designs, but nonconservatism of the method was not proved. Here, we prove nonconservatism in two designs based on the third method. Proving such nonconservatism is difficult using experiments or with large material nonlinearity in simulations. We first discuss these difficulties to motivate our approach. We then present two examples: a spherical shell and a torispherical shell, both under external pressure. The shell walls are thin enough so that plasticity is not encountered before structural collapse. For specific shape imperfections, we show with geometrically nonlinear, purely elastic, highly refined, post-buckling analysis using abaqus that the physical loads at which the imperfect shells collapse are overpredicted via RCC-MR's third method by factors of about 8/7 and 11/10, respectively. We emphasize that code-based design using nonlinear simulation prescribes a further safety factor of 2.5, which we have denied ourselves here in order to give the third method the benefit of doubt. We conclude that the third imperfection quantification method in RCC-MR should be reexamined.