you are assuming that amount of light falling on two does not influence the outcome... you might gave a grey object illuminated so that it will reflect more light in the end than white object... plus 12.7% is how spot meter assumes the reflectance of the target (and it varies - you need to check how your camera model meters, even around 12.7% is how most of them do), not actual reflectance of the gray reference.
You're creating random situations, and that's of no help. Exposure is based on the light source. When you have a single light source, setting exposure by spot metering a 12.7% card (or equivalent, compensated reference such as an 18% card with +0.5 EC applied) will give you an exposure where white (90%+ reflectance) will be near saturation...always.
When a scene has two light sources then you have to start making compromises. That's what you have in outdoor scenes where part of the frame is lit by direct sunlight and the other part is in open shadow (the sky glow is the light source, which is why light in open shade is so blue.) In such a case, you have to decide what's important and adjust exposure accordingly. But just because such situations exist doesn't mean we toss the basic knowledge. A gray card is just a tool...but a valuable one if you understand how to use it.
And the 12.7% doesn't vary. Otherwise, you couldn't use a handheld meter to set exposure.
There's a youtube video of some guy attempting to demonstrate how to calibrate a Canon 7D to a Sekonic meter. It's terrible. But although everything he did was wrong, the video indirectly demonstates that the 7D, Sekonic, and another Minolta meter that he used were all calibrated exactly the same way (before he ruined the Sekonic with his "calibration".) Nikon is also 12.7% gray.
I keep hearing that exposure varies but I never see it demonstrated. On the other hand, I know that if you spot meter a white or gray wall, the metered area will be rendered as sRGB 100 (before any processing) on Canon, Nikon, and Pentax at least (and Sekonic meters will give the same exposure values.)