Thanks chaps - I stand corrected. Have had a look at that tatty bit of cardboard issued by the FAA and it does indeed state as you say. Can't go crop-dusting though. Oh dear, what a pity, never mind!
Simple enough - valid UK PPL with SEP Rating plus that bit of Uncle Spam's cardboard means it's OK to fly under PPL privilieges in the US. Anything less - perhaps yes, perhaps no, perhaps maybe......