My husband has worked in 2 different fast food restaurants (neither was McD's or Wendy's) and he told me as well that they used separate fryers for fries because the breaded items and all the stuff they shed into the oil would make the fries taste bad.
So these restaurants are going against protocol AND making a product taste bad. :-\
You might have a better response by telling them that you are allergic to wheat/flour (even though it doesn't tell the whole story) than by just stating that you have celiac. Your average fast casual food employee isn't likely to know what celiac is. That could have been part of their confusion.