Thank you!
I should stress that my explanation is a gross simplification, and some of my examples might be a little off. Further, the specific role varies from jurisdiction to jurisdiction.
The key takeaway: The role of the coroner is (generally) closer to that of the prosecutor than it is to that of the medical examiner.
There is no such word as "its". That archaic usage was an exception to the "appostrophe-s" construction used to indicate possession. Deprecating that usage eliminates that unnecessary rule exception. While abandoning this antiquated rule does create a homonym, the contractive or possessive meaning is clear in context, as your criticism clearly demonstrates.
"It's" is both the contractive form of "it is/was" and the possessive form of "it".
Only English teachers and similar obnoxious, gatekeeping pedants mourn the loss of "its".