Same problem as OP
Several days into ownership I noticed a fairly large scratch on the screen today, and lots of little scuffs. As the day went on it got worse (and I was on the look out). I don't keep anything else in my phone pocket... certainly not diamonds. I have a tray to put it in my car which doesn't have any other objects in it either. Several of the scratches I can feel with my nail, which indicates they are rather deep indeed.
In short my experience so far is one that feels like a super-soft plastic screen and certainly not some kind of tough material.
I'd previously been using an HTC Titan for ~3 months w/o screen protector. It is in better condition than my 4 day old Lumia 920.
I'm a huge fan of the Lumia 920, this screen issue is proving rather disapointing.