I would not have thought so. If BA think that tickets to/from certain destinations can be dodgy, it would need to make its enquiries before concluding the contract and I can't see any reason whatsoever why their systems could not be set up to do just that. If they have been happy to take the passenger's money and issue the ticket, and in the absence of any irregularity in the payment or improper behaviour by the passenger, it seems to me that they are not on strong grounds to deny boarding and refuse to carry the passenger.