IMHO, it seems like the applicant has all of the qualities of a loan and the income is not really an issue, but an excuse not to make the loan. It also appears that there are other circumstances (rather than the income, but the income may be the easiest to explain) not to make the loan.
Deny the loan and document the file for the actual reasons for a regulator. (Remember, that it may be discoverable in a court case). Send an AAN indicating that the loan is denied, and give the applicant the option of asking the bank for the reasons. If not, see Sox in '13.
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Integrity. With it, nothing else matters. Without it, nothing else matters.