Tires do dry rot. It there is no crack in the tire they should be safe. I don't know of any law. They probably worry about liability and they make money on new tires. Try a small independent shop.
I don't know about any law but if the tires are more than ten years old and have mostly been outside, I would change them.
If the tires aren't safe to drive on, they might not be allowed to let someone drive it off.
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