I'm not totally sure what the GP meant, but I think it has to do with the owning/operating organization of the plane not being a qualified (Part 121/135) company for commercial operations.

A grandfather-in-law owned his own small business (a civil engineering firm), and had a plane that he flew to get to meetings/job sites across the Midwest. He could fly company employees just fine- and the company could reimburse him for the flight expense, and since it was not for the public that was fine. He could fly his family or friends on his own dime just fine. But if a family member or friend not working for the company tried to compensate him for the costs, then it is a question of "is his company actually an unlicensed airline?" and now we're getting into territory where it gets complicated. The FAA heavily regulates airlines, which is a major reason they are so safe. But there has to be a lower bound on what gets regulated, and avoiding that is what I think that GP is referencing.

That makes sense, at least as a partial explanation. Thanks.