I think I'm going to write up a paper and post it on the internet. If it's there, it has to be true, right?
I've had a couple wheels crack over the years, none with a radial tire mounted on it.
If this were accurate and a concern, along about the mid to late '70s we would have seen a rash of wheel failures. I worked in a station with a tire shop in the back that sold a lot of BF Goodrich radials, almost all mounted on wheels that originally had bias tires on them. I did the tire repairs for a year. I never saw a failed wheel with a radial tire on it. The only failed wheels I saw were a couple that were rusted so that they cracked along the outer lip where the tire mounted. None were a catastrophic failure, they were flats where the crack was noticed while it was dismounted.
I did see catastrophic failures of tires - I recall one guy where I had to round up another spare. He drove over a broken Pepsi bottle which took out a 3" dia plug from both his front and rear tire. I saw blowouts where radials had lost the whole sidewall, dropping them straight to the ground. I saw sidewalls cut clean through where they hit a curb - but in all cases the wheels were intact.
If you have wheels that were severely rusted at one time, I'd be worried a bit. Deep pitting, bent and straightened I might take a closer look. By the way, there is a whole industry doing this from the back of trailers - they have to leave a wheel weaker than they found it and I haven't heard of them being a problem.
I think this is a lot of smoke with no substance. If you're going to worry, I'd be a lot more concerned with the extra stresses put on the front end parts by the extra traction of the radials.