Regional aviation differences never stop surprising me.
When I was keeping paper log books I had a column for entering PIC hours. If the PIC column was empty I was not PIC and entered the hours as instruction received. The person who was PIC signed that log entry.
Why would I ever need to say that I, self, or me was the person logging PIC? My logs are for my flight time not for someone else's.
There were never enough columns in a paper log for me to record and total what I wanted and that's one of the reasons I abandoned paper logs in favor of computer records.