Continental
seems to be moving towards
Yaatri's interpritation of the Carrier Access rules.
Formerly, the website was very clear that the manufacturer's label certifying compliance was required. Now, it shows some flexibility.
(CPAP) machines may be carried and used on board Continental and Continental Micronesia flights if it can be verified by a manufacturers’ label or otherwise that it meets applicable FAA requirements. (emphasis mine)
However, the "Ask Alex" feature still uses the old language.
CPAP machines, respirators, and ventilators approved by the FAA may be carried and used on board our aircraft at no charge. The device is required to display the manufacturer's label indicating it meets FAA requirements. For more information see this page. (emphasis mine)