getting back to the OP, the instructions from the grey card itself reads:
"Meter readings of the gray card cshould be adjusted as follows- 1) For subjects of normal reflectance increase the indicated exposure by 1/2 stop. 2) For light subjects use the indicated exposure; for very light subjects decrease exposure by 1/2 stop 3) If the subject is dark to very dark increase the indicated exposure by 1 to 1.5 stops"

So to answr your question, the grey card is actually designed to be lighter than 'middle grey'.