Not necessarly true.

You can use AA miles on BA flights to UK from Canada, Mexico, and Caribbean. Since you want an award ticket, your connecting flight to one of the locations listed above would also be included.
If you said, "oh never mind, I just found out I can't use AA miles on BA non-stop between ORD-LHR", then you would be correct, but if you are willing to do ORD-YYZ(AA)-LHR(BA) then it's possible.

Also AA & BA is allowed to codeshare on few flights between US and MAN. BA has JFK-MAN which allows AA to codeshare. You are allowed to use AA miles on that route. You will also earn AA miles according to AA rules if you purchase AA coded flight.