The website is a good example of why attempts to simplify language often don't work.
Under US law, the baggage allowance (not waivers for status) of the marketing carrier of the first segment of the ticket, apply to the entire ticket. As an avios ticket, this is BA-marketed and thus the BA base allowance applies. That is a net positive because a standard Y ticket on AA would not have a baggage allowance.
As to waivers for status, that is in the province of the operating carrier and, in this case, the AA allowance for OWE would apply.
This should all show on the e-ticket receipt and it is that allowance which the check-in agent will see when you present the bags. If it shows up wrong on your e-ticket receipt, get it corrected now.