I encountered the same “Check Document country of issue” problem when trying to check in with IB, either through the IB mobile app or online, on an AA transatlantic award with the first segment an IB-operated domestic segment in Spain. I shouldn’t have to enter any visa information because I am a U.S. citizen traveling on a U.S. passport, but I too had to resort to the trick of also entering my U.S. passport information under the visa section.
FlyerTalk to the rescue! Thanks, folks.