Ah, I see. It's not about physical or not, but trött is something that you are, but ilska is not something a person can be, it is just the word for the emotion itself. A person can be arg 'angry'.
So it depends on the kind of word:
Jag känner ingen ilska 'I feel no anger'
Jag känner mig inte arg 'I'm not feeling angry'
Jag känner mig inte trött 'I'm not feeling tired'
Jag känner ingen trötthet 'I'm not feeling any fatigue'
I think the point being made is about the use of the 'mig, dig, sig etc' in concert with känna and the effect on meaning. And if not, it what confuses me here. As i understand it känna sig means to feel an emotion, and kānna on its own means know. Common Swedish Verbs by Hensleigh (which is fantastic at listing many verbs, eapecially those with a particle), aslo says känna means 'feel' but i thought in the sense of 'touch'. So the use of ingen here with känna, I would expect sometjing physical or figurative I could touch but can känna mean feel (an emotion) when used with ingen. Apologies for the somewhat long-winded query!
I'm years late to this thread but I've got the impression that känner only means know in sentences like 'Jag känner henne' and if you talk about knowing things in general it's 'Jag vet' -- is this correct, or are those just the only sentences I've happened to come across here and känner is actually more versatile?