The actual closest that we can get to the horse's mouth is a 1951 LA Times interview with Mathieu. The article was written on the occasion of Philippe's relocating to make way for the Hollywood Freeway.
“One day a police officer asked me if I would mind splitting one of these large loaves of French bread and filling it with 'some of the delicious roast pork,'” said Mathieu. “I was not too busy, so I said, 'Sure.' Then he asked me to 'please cut it in half. I've got a friend outside who can eat it.' Then he asked for some pickles, onions and olives.”
The sandwich was born and awaited its dip.
"Then we started making French-roll sandwiches for those who had smaller appetites," Mathieu said. "One day a customer saw some gravy in the bottom of a large pan of roast meat. He asked me if I would mind dipping one side of the French roll in that gravy. I did, and right away five or six others wanted the same."