This issue has been settled conclusively. Deduction or no deduction, public benefit flying can be flown under Part 91. The Air Care Alliance page has a thorough explanation of the ruling. CFI's and CFII's can participate, too. Most PBF organizations allow instructors to claim BFR's and Instrument Proficiency Checks to other members as donations.
Public benefit flying organizations have an amazingly good safety record.
Patients are urged to make backup plans in case of a weather delay, so the PIC decides if the mission goes as scheduled. Joe is a regular contributor to AVweb.