The FAA letter to EAA and AOPA discussed here was in stark contrast to prior written policy and according to EAA will likely be rescinded or considerably rescinded in next couple of weeks. The letter was intended to deal with limited category training (a lot became of this issue after a war bird that takes donations for passenger flights crashed), but somewhere along the line got off track and even added other EXP and primary categories to it (the regulatory reason for primary was for training with compensation in the first place).
From FAA FSIMS online documents
3-292 FLIGHT TRAINING IN EXPERIMENTAL AIRCRAFT.
A. Use of Experimental Aircraft for Flight Training. Persons may receive, and provide compensation for, flight training in an aircraft holding an experimental certificate issued for any of the purposes specified in § 21.191. Other than the person receiving flight training, the operation must not involve the carriage of persons or property for compensation or hire or be prohibited by the aircraft’s operating limitations.
B. Flight Instructors. Flight instructors may receive compensation for providing flight training in an experimental aircraft, but may not receive compensation for the use of the aircraft in which they provide that flight training unless in accordance with a LODA issued under § 91.319(h) and as described in paragraph 3-293. An experimental aircraft owner may not rent an experimental LSA to a person for the purpose of conducting solo flight.
FAA written policy allows for primary and advance flight training in all categories of experimental aircraft (ref FAA order 8900.1 for starters), and the instructor or examiner can be compensated (you can’t charge for plane unless FAA issues a letter saying you can, and will only do so for type specific transition training).