I recently called a restaurant to ask whether there were any menu items they could guarantee were dairy-free, or at least had minimal risk of cross-contamination. Whoever answered the phone said they would check the gluten-free menu.
I didn't ask about gluten. I asked about dairy. If I ask about dairy, I also don't need to know about eggs. Dairy is from the animal that says "moo," not the animal that says "cluck cluck." I shouldn't feel this burning rage at a kindergarten-level explanation, but I will certainly not eat at that restaurant.