Would you trust 13 year old tires?

The basic problem with tires is that they decay from the inside out, so they may look fine on the outside, but the inside is deteriorated.
I recently sold my 2004 Corvette Z06 that I bought new and sold with only 1,500 miles with the original tires that looked like they
just rolled off the showroom floor. So, 12 year old tires, but I did have concerns about their age. Sold car before I had to replace them,
and that would have cost around $1k or more.