I´d agree with you that checkmytrip is incorrect. I´ve never heard of any special agreement between BD and AC (or any other airline for this matter).

A non-status pax travelling on AC metal definitely is only allowed one checked piece of baggage on Europe-Canada flights.

Regarding the Canada-US segments: If your tickets were issued before Sept. 7 2011, I´d think you´d be entitled to one free checked bag.
You could also try arguing that the Canada-US segments are part of an int´l itinerary, afaik this argument doesn´t apply if you had a stopover, but I´ve heard of many pax using this argument successfully, so YMMV.