The FAA takes a very strict stance in interpreting how and when pilots can be reimbursed for a flight.
§ 61.113 Private pilot privileges and limitations: Pilot in command.
(c) A private pilot may not pay less than the pro rata share of the operating expenses of a flight with passengers, provided the expenses involve only fuel, oil, airport expenditures, or rental fees.
In a letter of interpretation on June 30, 1993 they state:
The costs which may be shared includes only those expenses that would not have been incurred if the flight did not take place; for example, fuel and oil consumed on the flight and ramp or tie-down fees at the destination airport. These expenses would exclude such items as insurance, maintenance or other capital costs. To be in full compliance with the regulation, the costs must be shared equally between the private pilot and his or her passengers.
Moreover, in a letter of interpretation on July 19, 2010 and another LOA on May 18, 2009, they emphasize that the flight must have a bona fide common purpose. And the pilot must be reimbursed by the passengers, not a third party—like their employer or club.
They interpret compensation literally as well. In a letter of interpretation dated October 8, 2010 they state that:
The FAA construes the terms “compensation or hire” very broadly. It does not require a profit, profit motive, or the actual payment of funds. Instead, the FAA views compensation as the receipt of anything of value.
They conclude that a balloon owner’s offer of free dinner to the pilots and crew constitutes compensation for hire.
An FAA Safety Briefing the spells out their interpretation of the rules and states:
Goodwill obtained from providing a flight has also been determined to be compensation. Everyone knows how valuable a favorable news article or celebrity endorsement can be. Bartering can be considered compensation, too. You may want to think twice before you take someone flying in exchange for spending a weekend at their beach house.
Sharing expenses with a passenger on a flight to a place you would not otherwise be flying to would be a problem.