In which cases is it not true? Perhaps some examples might be useful?
If I had an AONE* or a DONE*, I cannot believe that any OW airline would refuse to give me a seat in coach on an all-coach flight (that was not oversold and had available inventory in any class). Are you saying that there are situations in which a OW airline would refuse to accept an A or D coupon for an available seat in coach?
From xONEx rules
Code:
(C) BOOKING CODES
FIRST BUSINESS ECONOMY
AA BA CX IB QF LA LP JL JO A D L
AY EG MA RJ XL 4M D D L
AY LA LP XL 4M Domestic Y Y L
AA Domestic Flights 3000-5599 Y Y L
JL Domestic Flights
(To/From NRT) J J H
JL/NU/JC Domestic Flights
(All other Domestic Points) J J Y
BA World Traveller Plus T
NOTE: When the class of service for the fare is not offered book in the next lower class of service
using the booking classes above.
EXCEPTION - For services within/between the USA and Canada where no D class is offered
Business class passengers may book and travel in A class subject to availability. This provision
does not apply on any flight where a Business class cabin exists but is unavailable for booking.
Thus BA CX IB QF LA* LP* JL* JO AY EG MA RJ XL 4M all book into less than full economy should first/business not be offered. Where first/business is offered but not available, even AA (excl flights numbered 3000-5599) books into less than full economy.
*excl domestic