Ownership isn’t required to use the death note. This is like when Ray Penber, the FBI Agent, unknowingly wrote the names of all the FBI agents on the page.
I think it also gets missed that when light forces/tricks others to use the death note he also prevents them from entering heaven or hell. Sending them to endless purgatory which is even more cruel that someone like Ray Penber won’t even be able to reunite with his wife in the afterlife.
P.S. I doom scroll so IDK how old posts are when I comment