Anecdotal. I have no problem with being careful, but they need to explain WHY they think it is the cause, not just spout urban myths because the symptoms seem to fit.
It may be coincidence that those two phones happened to die whilst being near that machine, I'll grant you that but would you want to risk putting your latest expensive mobile near it?
I can't explain how a microwave works either but I'm sure that that technology could fry more than just food.