I have a flight to London coming up and I want to figure out if I have free baggage allowance or not.

I have Alaska MVP (one world Ruby) which with AA gives me 1 free checked bag. My eticket says NO CHARGE for 1st bag.

However, while my ticket is issued and purchased from AA, neither segments are AA operated. It is basic economy (B class on BA and Q on IB)

My outgoing itinerary is JFK-LHR, AA 6929 (BA116)
And return is LHR-MAD-JFK, AA 8555 and AA 8837 (IB3169 and IB6253).

I called AA and they are convinced I have bags but when I call BA they say no bags. AA even left a note on my ticket saying I have Ruby status so I should have 1 free bag. BA said that because I have basic fare, I don't and for BA only sapphire+ has free baggage anyway.

Does the DOT regulation about marketing airline baggage allowances apply? Is there anything I can say to BA or IB to convince them I should get baggage?