"The only test that your scenario does not satisfy is 'compensation'"
The FAA and NTSB Board both view the accrual of flight time as compensation when considering whether an operation in common carriage occurred or is likely to occur.
See Administrator v. Blackburn, 4 NTSB 409 (1982) affirmed in Blackburn v. NTSB, 709 F.2d 1514 (9th Cir. 1983), Administrator v. Mims, 7 NTSB 850 (1991), Administrator v. Wagner, NTSB Order No. EA-4081 (1994), Administrator v. Murray, NTSB Order No. EA-5061 (2003), Administrator v. Clair Aero, Inc., NTSB Order No. EA-5181 (2005), Administrator v. Wallace, NTSB Order No. EA-5461 (2009).
See also Memo (May 1982) from Bernard Geier, Chief, General Aviation and Commercial Division, to Chief, Flight Standards Division; and the memo (18 May 2009) to Don Bobertz, Attorney, Office of the Regional Counsel Western Pacific Region, AWP-007 from Rebecca B. MacPherson, Assistant Chief Counsel for Regulations, AGC-200.
See also interpretations from the Office of the Chief Counsel for FAA to Judy Lincoln (30 Oct 1990) and to John W Harrington (23 Oct 1997).