Would you trust 13 year old tires?

I seriously doubt he's actually driving that car with those tires. Typically if cars like that are driven and shown they're driven with one set of tires and shown with another. Not only would it be a complete waste to total the car because of a tire blowout, but you don't want to wear out the original tires. If high end concourse cars are driven it's not uncommon for them to have a lot of extras, stuff they use to drive on the road and original or correct parts they use to show.

Most of the time cars like that are driven off the trailer and onto the grass anyway. If he is driving that car on those tires for any distance or at any real speed, well, he's gambling. Doesn't matter who he is. But he's rich, so maybe he doesn't care.
Tires use to last much longer. 5-7 now