It sounds like he didn’t actually file a false police report. They don’t even say they asked him whether it’s true. It seems the police just read a post by a random person on the internet, assumed it’s true, then arrested him when it wasn’t. The article is devastatingly light on info, though, so I can’t be sure.

Yeah, we can't actually tell whether the image was posted with the poster going 'hey, @SouthKoreanPolice, wolf is here!', or whether it was xit out without any comment or context, or whether it was in response to a friend who lives in the vicinity of the location in the picture wondering where the wolf was,...

I don't care enough to bother finding out, but seems like the BBC could have done some more journalism, if they were so inclined.

That was the impression I got as well, but it seems like other people disagree.