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.