More likely that the writer didn't know the name/gender of the officer who tracked her down.
Well, they could always read the Cleveland, Ohio paper to find out: “a Lakeland police officer downloaded the Periscope app on his personal phone so officers could see the broadcast.”
http://www.cleveland.com/nation/index.ssf/2015/10/florida_woman_uses_periscope_t.html
Incompetent writer, or an incompetent writer trying to be politically correct?
More likely that the writer didn’t know the name/gender of the officer who tracked her down.
In that case, I know that you know the convention has been to use the pronoun “his” when the sex is unknown but the number is known singular. Of course, one could say “his or her” but that’s cumbersome. Both are more correct than “their.”