Originally Posted by KodiakRS

Pilot flying does not mean pilot in command . If you are the FO you are earning SIC and only SIC regardless of who's physically flying the airplane. PIC has nothing to do with flying and everything to do with being the individual responsible for the operation of the aircraft.*

I would be extremely careful about telling a rental/insurance company that you have a bunch of PIC time that's not actually PIC. If something happens they could very easily construe this as "pencil whipping" your logbook and you'll very quickly find out that aviation lawyers are only slightly less expensive than aviation lawsuits.

*The one exception to this is when a line check airman is giving IOE to a not yet qualified captain. Things get a little fuzzy legally with who is responsible for what but IIRC the CA candidate still logs SIC. Ask a LCA if you want to be sure.