Metamerism is an effect that's usually (in photography) associated with viewing prints, especially ink jet prints. Dye based inks, and to a lesser extent pigment inks can appear to be color shifted depending on the type of light they are viewed under. This effect varies with the ink formulation. I know of no way to control or minimize this at the 'taking' end of the process.
What viewing the gray card in two different ways does do, however, is account for metamerism in the gray card by taking a measurement off of it when it's lit by the light illuminating the subject and then by the light that's hitting it from the point of view of the camera. Sometimes these are the same (in a studio for example) sometimes they are not.
In printing, one can compensate for metamerism by viewing a print under the light it's likely to be seen and correcting the colors accordingly. It's possible that photographing a gray card at different angles also gives a neutral-light and a neutral-dark that allows easier compensation.