Well, I've used our home oven for shrink plastic, Fimo etc. often enough, and as yet no-one has died.
I don't see why this would be an issue unless you maybe do something supremely stupid like put the plastic straight on the oven shelf so it melts and sticks and burns... and then you either a) clean the shelf or b) replace the shelf. These things don't usually produce fumes at all if used properly, and even then there's no reason it should do any permanent damage.
These things are designed to be used by kids and usually have a label saying "non-toxic" on them somewhere. I'd suggest that this was just a bit of panic-mongering, myself.