But it sounds like I can sit right seat in an acquaintance's single pilot jet...?
Some of your replies to the responses indicates a bit of over-thinking something pretty basic.
So long as your role does not involve being pilot in command or a required (by the FAA) crewmember, you can do pretty much anything and it does not matter which seat you are in unless the aircraft has a limitation requiring the pilot in command to be in the left seat,
Some of the things you can do:
Be the sole person hands-on flying so long as the pilot in command allows it (and the aircraft doesn't require two pilots).
Receive instruction.
Give instruction, even a flight review, to a pilot who is capable, willing, and current to act as PIC.
Be a passenger.
Some of the things you can't do:
Be the second pilot in an aircraft that requires more than one pilot.
Be a safety pilot.
Give instruction to a pilot who is under the hood.
Give a flight review to a non-current pilot.
Train someone for the HP, complex, or tailwheel endorsement.
Notice that there is one and only one thing differentiating those two lists. Your status as PIC or required (by the FAA) crew.