Would you trust 13 year old tires?

here in califorina . if its 6 years old or older . tire shop will not do anything but dismount it . i run 10year old tires on the rears . try to keep fresh rubb'r on the noise . just good for a driver . now show stuff , i would like to know how my insurance company sees the issue . tire costs are far less then replacement of a restored car , as well as all the other vintage rods n rides outthere . its funny that i change out front rubb'r faster than the rears , its seems the fronts all ways get issues before there wear out . just key'p da rub'r syd down my friends . burn'm if u can .