Here we have two ‘synthetic’ Color Checker Classic charts with artificially created 'to X-Rite spec' sRGB color swatches. There are transparent ‘holes’ punched through.
Underneath on the left is a reasonably exposed and un-doctored photo of a color checker shot in noon daylight and on the right is the same shot but with a ‘curves’ modification to balance the grays.
The base shot is developed in ACR with Adobe standard profile. It might look pretty but obviously isn’t all that accurate.

EDIT 120520: Instead of balancing the grays with an RGB curve, I used a more complex 'curve' using each of the three channels. I thought it might help.
It creates a perfect gray match but the colors that vary the most in the 'see-through' are visually similar to what you see in this chart.