it should, it is correct, and idiomatic. Report it.

It's all in the context. If you want to specify gender, you could use "ei" for hers and "lui" for his. Many times though, său/sa/săi/sale is used to refer to the subject of the sentence. For example, "El citește cartea sa" (he reads his own boom) vs "El citește cartea lui" (he reads someone else's book). This rule isn't concrete though, and many people don't follow it.