There's quite a kerfuffle over on c*cktalk about this.
Dyneema and nlyon slings are safe to use in appropriate application. They seem to be addressing an issue that came about a couple of yeas ago. As I remember a tragic accident occurred whereby a climber who had a sling cowstail (very common amongst climbers), clipped into a belay (possibly a bolt - it was in Europe). They stepped up to adjust something and slipped. The fall factor was somewhere approaching a FF1. The sling snapped. This scenario was replicated at Plas y Brenin. Again the slings snapped. Lots of people were surprised at this outcome - how I really don't know ?
Now it seems that the message has muddled people. If you're climbing using dynamic ropes and fall onto a sling (such as would be used on a quickdraw or thread/spike) the sling won't snap. The rope absorbs the energy.
If you're using sling cowstails when climbing - don't use them for fall arrest in the very specific situation mentioned above. If you wish to use them in a work positioning i.e. hanging off them; then do that, just don't introduce any slack.
Top bit of footage by the DMM boys (good to see Streeky's still got some hair!!)
Something not touched on was what the human body can take. This makes interesting reading (despite being from the HSE) relating to what sort of force our bodies can take; 6kN and we're broken!