"his own dog" has to be accepted too, it is closer to the Romanian meaning of the senence, which actually means nothing else. The English sentence without "own", may have the meaning like Jim kills John's dog, which is not the case for Romanian, which is more specific, the "își" pointing to "himself", or "his own".
OTOH, we subscribe to the general discussion that more positive sentences should be used... https://youtu.be/mcZLZF-jVEQ?t=207
Leave it to the Romanians <they have somebody kills his dog> The French have with the prisons. We are covered really well with the vocabulary in case we want to write a crime story.
Nu pot să cred că cineva s-a găndit să formuleze o asemenea frază, doar ca să folosească util cuvintele...eu cred că este făcută tendențios!!! Urât... Putea să formuleze de exemplu zicala "El îşi omoară timpul..."