A former brilliant student of mine, Hayden Parker, informed me that the head of safety matches are not made of red phosphorus.   Science Theatre at Michigan State University explains.

A "striking surface" is made of sand, powdered glass, and a chemical called "red phosphorus". The head of a safety match is made of sulfur, glass powder, and an oxidizing agent.

This is why safety matches cannot be lit on any surface.  The striking surface contains the red phosphorus and not the match itself.