"....... but has there ever been a documented case of a Paramotor injuring any Third Parties ?"
Don't know but there but for the grace of.... etc I could have gone...
About eight years ago returning from the west country to North London, at FL050 I was south of Lyneham, north of the ranges and receiving a radar service from Lyneham in good viz etc. I decided to go round a bit of Cu instead of thru' it, and thank God I did, On the other side of it at exactly my level and about 300m from the side of the Cu was a paramotor. Presumably no radio, not painting on radar etc. Would have been a nasty mess for both of us!