Is it possible it was a codeshare or oneworld alliance aircraft, so it could appear to be a BA booking but operated by someone else?
As far as I can see, from IST, the answer is no.
There are no 3rd party B767s flying for BA in BA cols.
Is it possible that the gentleman got his a/c type wrong?
BA do have some 2nd hand B737s, although none of them is ex American Airlines.