If that CFI is correct then you also could not conduct business when you
returned home, because you had flown home.

That said, the issue has not come up much previously, because the only
people who could not fly in furtherance of a business were student pilots
and recreational pilots. A student pilot who conducted flight in furtherance
of a business likely would have his solo endorsement revoked by his
instructor and that would be the end of it. He would have a tough time
explaining it to his next instructor.

I think the FAA would be concerned if you were making regular business trips
as a sport pilot, especially if you were carrying employees or delivering
supplies or customer orders. I doubt very much the FAA will hang you for
talking about business with your partner while you are up at some mountain
lodge unless the bulk of the time was spent discussing business.

Usually the issue comes up the other way. Someone wants to deduct his
business travel and has to show that the flight was in furtherance of a
business, or they are trying to avoid some state tax on non-business
aircraft. In that case the respondent has had to show documentation for the
business purpose of the travel, usually by showing that he carried employees
or other items for the business and that this was the main reason for
getting an airplane.

If you are deducting your airplane or seeking some other business tax
advantage it might be very hard for you to then tell the FAA that your
flights were not in furtherance of a business.