Would you trust 13 year old tires?

I just watched an episode of Chasing Classic Cars where Wayne bought a mid 50s Studebaker that he claimed was totally original including tires.
This car will only be driven when going to a show, so I guess these 60 year old tires are safe for this application.
They looked to be in really nice shape (wide whites), as the car had only 7,300 original miles. What a beauty.
Looked like it came from a time capsule.