If it was as clear cut as you suggest. Why do operators bother with the not insignificant expense of having an AOC?
Because they wish to promote and operate an air transport service. I am not proposing to do that.
Your friends,friends of friends, or clients are NOT aircraft owners. You're not flying them in direct connection to THIER business, you're flying them in direct connection to YOUR business. Clearer?
No. As discussed, it is legal for a third party to hire an aircraft and then hire or ask a pilot to fly the aircraft. As long as all parties are properly insured, and the pilot is licenced to fly the plane, then it is fine. The question of the purpose of the flight and what business may be done outside the flight is irrelevant.