Where do you get "shared purpose"? Where does it say the pilot and any passengers have to have the same purpose for it to not be an illegal charter?
FAA Legal opinions and NTSB case law consistently saying so over the past 30 years or so.
Like,
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Section 61.118(b) [same reg, earlier numbering] allows a private pilot to share the operating expenses of a flight with his or her passengers. Additionally, the FAA has interpreted 61.118(b) so that the only allowable share-the-costs operations are those which are bona fide, that is,
joint ventures for a common purpose with the expenses being defrayed by all passengers and the pilot. - 1985 Legal Opinion
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or, one of my favorites, from 1977, involving a a "no" answer to a pilot who wanted to transport a candidate he wanted to help win for a share of the expenses
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it is not a joint venture (you are not running for office)
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Or, maybe you want one a little more current. How about this from a 1994 NTSB decision upholding a 45 day suspension of a commercial pilot certificate for transpoting TV crew:
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Part 135 compensation or hire . There is a clear public interest in ensuring that only properly certificated commercial operators perform commercial services. Administrator v. Carter , NTSB Order EA-3730 (1992). Although an exception has been created to permit certain operations under Part 91, where passengers contribute to the flight cost, to be performed without compliance with the stringent training and proficiency rules of Part 135, that exception is a narrow one. Otherwise, stricter rules in Part 135 (concerning for-hire operations generally in smaller aircraft) apply. See 49 C.F.R. 135.1 and Administrator v. Sabar , 3 NTSB 3119, 3120 (1980).
Expenses may be shared only where the pilot and the passengers share a common purpose in the flight. Notably relevant here, in Administrator v. Reimer , 3 NTSB 2306 (1980), we found that there was no common purpose in a pilot sharing expenses with passengers, when the pilot's purpose was to gain flight time and the passengers' purpose was to skydive.
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BTW, in that case, there were two pilots who were violated. One of them claimed that he didn't know the other pilot had an arrangement with the TV crew. He claimed he was a CFI and was
just giving flight instruction to the other pilot. Funny. Isn't that where we started?
Here's that last case:
http://ntsb.gov/alj/alj/O_n_O/docs/aviation/4306.PDF You might even see just how hard it is to prove one of these. I have no doubt that you can read it and find 20 reasons why it wouldn't apply to =you=. But then, I'll leave it to you to find 20 other times where the NTSB or FAA Legal upheld the exact same principle.
Funny that your DPE didn't mention those or the many more like them.