I don't think you're right NE... the student, even if a Private pilot, can't take the plane up solo if they wanted to because they are not rated to. Just like a pvt pilot can't go IFR solo without their their instrument RATING. It's the same difference. So logging PIC in a plane that you can't fly solo in because you're not rated to just because there is an instructor along isn't right.

When I flew in an extra 300 I didn't log PIC. I had HP and my pvt but it's a tail dragger and I wasn't rated to fly it so I can't be PIC period.