Here's a hypothetical game:
Citibank ties John Doe's 4147-11XX-XXXX-XXXX VISA credit card number (all Citi AAdvantage VISA have BIN number that starts with 4147-11) with his AAdvantage number, say it's ABCD123.
Every month (at least if John uses his AAdvantage VISA card), Citibank reports the miles earned from that credit card and deposits the miles to John Doe's ABCD123 AAdvantage account.
Likewise then, wouldn't the opposite be true? If miles gets deposited to American from Citibank, shouldn't American then know that John's is also a Citibank VISA cardholder?
IF John Doe Citibank cardholder 4147-11XX-XXXX-XXXX miles -> John Doe AAdvantage member ABCD123
THEN
John Doe AAdvantage ABCD123 = John Doe Citibank 4147-11XX-XXXX-XXXX
As such, there has to be a system somewhere in AAdvantage that says John Doe AAdvantage member ABCD123 is John Doe Citi VISA cardholder, therefore, give the John Doe all the Citibank VISA benefits when traveling on AA whether or not he used the VISA card to pay for this particular trip.