Don't believe me then try booking a seat to New York.
I just did. And as soon as I entered my from and to dates the offered flights for those days correctly state which airport is being used for each flight. And flights to Moscow (first place I could come up with of where BA do not use the airport you first think of) likewise specify Domodedovo. And the BA timetables for these places correctly explain the airports used.
Come on, guys, the same as my comments about the Wizzair timetable applies to us all here. Let's try and be accurate.