No it hasn't happened to me. However (and I think this is what you are getting at), thanks to a New Zealand crash investigation TV show, I am aware of old tyres that may look like they have plenty of tread but are actually out of date and dangerous.
My CT has tyres that must be 11-12 years old and everyone that I've asked reckons 'no worries' as they're not on the vehicle doing the driving but simply being pulled along behind. But I'm not so sure. Now reading your story I'm even less uncomfortable.
I've got my name down with a local tyre distributor who reckons they get okay off road trade-ins from time to time and they'll call me when they get some. I'll rest easier when those tyres (and the spare) are replaced with something made this century.
Wayne