The FAA will dispute that when asked, but I think that assessment is correct.
The only issue is when StrateandLevel talks about "any of the privileges". An N-reg aircraft cannot be used for Public Transport or Aeria Work, other than in connection with a US-based air carrier exercising its ICAO rights.
The JAA ATPL can fly an N-reg in the UK only in connection with non-commercial flying.
2D