City of Heretics - Heath Lowrance

"Peter Murke was sitting on the edge of my cot, watching him."

I like the story, but sentences like this are driving me nuts, and those are a rather frequent occurance. How does this work exactly when you have a third person narrative, and then a first person POV (that of the main character Crowe) slips in mid-sentence?

Both, "my" and "him" refer to Crowe. So confused. I would think it should be "Peter Murke was sitting on the edge of his cot, watching him.", no?