The plan includes replacing the medicine cabinet, which is wood framed and continues the country style look of this other wise metropolitan home. A recessed cabinet with framless mirror sure would look great - flush with the wall. But there's a reason people don't do this - venting. Apparently, sink plumbing must be vented out the roof. This venting takes the form of heavy duty 3" steel pipe in many cases, and runs right up the wall where your recessed medicine cabinet would best go.
Here's a little view of what the venting inside our wall looked like, and possibly what yours might look like too. We'll see a lot more of this subject later on. In our case, it only limits the width of the medicine cabinet we can recess without far more extensive and expensive work.