Sorry for not providing more information. My wife (US citizen as I am) attempted to board the flight back to Costa Rica (return trip; San Jose-LA-San Jose), when she was refused passage, until she purchased another ticket. AA quoted Timatic information with language I previously left. Unfortunately, AA did not suggest she purchase a refundable ticket, so she purchased a round-trip ticket from America West. (I now understand that a refundable ticket would have been the quicky solution, but my wife didn't have that hindsight.)
I talked with AA about an overly narrow interpretation of Timatic information. They remain rigid. America West contacted immigration in C.R. and found that a letter from the marina, where boat is docked, satisfied their intent (evidence of ongoing travel). AA refused to call immigration, but relied on the Timatic language. When I phoned C.R. immigration, they had no difficulty in accepting any sort of verification of ongoing travel arrangements. So, the block seems to come from AA, not from C.R. immigration.
Since we intend to travel by boat from C.R. to Panama, the ticket she purchased does little good (America West does not fly out of Panama) and returning to C.R. to catch a future flight is a giant nuisance.
I understand that violation of immigration laws opens airlines to fines and extra costs, but AA is relying upon indirect information (from Timatic service) rather than direct verification from immigration.
Interestingly, AA does not enforce the other Timatic requirement, that all passengers "hold sufficient funds." AA doesn't ask to verify how much money or credit each passenger has before boarding.
This problem seems to affect all US citizens who originate their flight in C.R. and visit the US, such as the cruising fleet.
I obtained the Timatic information from Delta Airlines online.