Literally, sure, but isn't it like "ont i ryggen", not "ont i sin rygg"? You know the back is his because of context, even though there's no possessive, whereas you would be much more likely to make the possessive in English. I'm sure you could construct a scenario where the readers weren't those of the newspaper, but it seems to me the most natural interpretation is that they are, and the most natural way of expressing that in English is with the possessive.
I'm not arguing — I fully realise my grasp of Swedish idiom is tenuous! I'm just trying to understand what's happening.
I absolutely get your point. These idiomatic nuances are tricky, and not all natives will agree on them - so it's no wonder learners need to go through some trial and error.
The thing is, a phrase such as this one sounds like something you'd find in e.g. an article comparing different newspapers. Maybe there was a poll like "what's your favourite newspaper?" where paper 1 got 81 %, paper 2 got 15 %, and paper 3 got 4 %. The article could then write that paper 1 was loved by the readers.
It's a made-up example, but I think it illustrates why it's not clear enough that it has to be the people reading the paper. Of course, in proper context "its" would be perfectly appropriate.
Does that help?