Interesting to see that someone else was confused by BA stating you should check with other carriers (American in my case). They confirmed that BA Baggage rules applied on BA1515(AA104), though they have carry-on as 23kg 101cm, no mention of the 126cm size bag.
British Airways clearly doesn't understand DoT 399.87 in respect to carry-on baggage, which probably is the reason for the "check with other carriers" line and link. BA emailed me saying they "did not believe the rule applied to carry-on baggage". I got confirmation from Tim Kelly at DoT saying it did.
"Section 399.87 does apply to carry-on baggage; please see FAQ #51 on page 41 at
http://www.dot.gov/sites/dot.gov/fil...EAPP_2_FAQ.pdf. For international passenger itineraries, see also FAQ #37 on page 36 of that same webpage. Note the distinction between a “code-share” passenger itinerary (where a given flight is held out in the identity of one airline but operated by another), vs. an “interline” itinerary (where the flights in the passenger’s itinerary are operated by two or more airlines but the flight at issue is not a code-share)."
The whole idea of DoT rules 399.85 and 399.87 is clear information at every stage of booking and on the eTicket, without the hassle of having to check with each carrier and know which flights are operated by another carrier.
I think BA have filed incorrect/incomplete information on ATPCO's published list of US DOT Carriers, but don't know how I get it resolved.