That is the issue right there. Please read the Help for the Award & Upgrade results page, which under the AA section states:

•When searching for award/upgrade inventory to a destination that AA doesn't fly to, it is best to only do the search for segments that AA itself operates, and not include the segments that it doesn't. This will insure the most accurate results.

As such, a LHR-JFK award search properly returns T0.

We are working with our GDS provider to exclude the code-shares in the results so that code-share options are excluded, in which case your BCN-JFK search would only have shown the AA non-stop, not any options to connect with BA flights thru LHR.