You're referring to the Brochet experiment? That wasn't a blind test: the white wine was dyed red with a flavourless dye, so there was an element of deception involved.
Biased sample. There are many confounding factors why if you cannot tell the difference, it is likely your family can’t either.
I do like the idea of testing my wine drinking friends, who are definitely not snobs. I would bet money they would mostly pick the difference between a normal: Oaked Chardonnay, Reisling, Savignon Blanc, and Cabernet Savignon. I suspect the red wine drinkers could tell some of the red wine varietals too (I would struggle there).