Part 91 ops, unlike Part 121/135 does not require a "designated" PIC. So if you are operating an aircraft that is type certificated for more than one pilot, I would say you are "acting as PIC" if flying from the left seat. Many companies, EJA included I believe, allow seat swapping.
You believe wrong.
EJA designates a PIC and SIC on every flight.
Every EJA flight has a dispatch release.
Also, the "designated" PIC as you call it, not only has to worry about the FAA, but the company as well when things don't go right.
Many times we fly Part 91, but everyone at the company is
Part 135 qualified with a PIC or SIC checkride.
These positions are bid upon and awarded, by seniority.
We also swap seats as you call it, but technically, as per the PIC's discretion. There are minimum hour requirements in our GOM that we follow.
98% of the time we do swap, but again, technically it is at the PIC's discretion and only when we ferry with no passengers.
Sweat the PIC checkride at EJA, and you get to log the time after being released as a PIC.
P.S., not to many Falcon 2000 and Citation X's are scheduled to be single-pilot authorized.