And with most states requiring tires be no older than 5 years (to be legal anyway) it's an expensive additional hobby expense for sure.
My local tire shop fed me that line of crap too. When I researched it I learned that there was no such law in my state. The whole thing was a scam by my tire dealer to avoid liability and sell more new tires!
There is no definitive amount of time that tires became unsafe; there are just too many variables. Generally 5-6 years is the RECOMMENDED time, but there was no actual law in my state, only individual businesses policies. If the rubber still appears pliable and there are no visible cracks, tires should still be safe. Thanks to my research I found a local company that would install some 25-year-old Goodyear Invictas off a classic Corvette onto my daily driver. With the donor car locked away in a garage, the tires had minimal mileage and had never seen any sun. They've been great tires for about 40,000 miles now and counting.