I'd mention the spread of foot fungus from child to child, she may not get what you are saying.
I have one DCM I practically have to give a photo menu to about everything.
She may be more concerned with sweaty feet causing odor and discomfort rather than cotton socks reducing the spread of the fungus from person to person. She is maybe wanting the childs feet to air dry during nap. Some also believe that wearing shoes damages children's feet.
Not enough people seem to know that wearing the same pair of shoes everyday is a bad idea (they should be allowed to dry 24 hours, alternated) and socks minimize the risk.