I agree with you DC.  Frank might have been taken, and might not have been.  But his heart was in the right place.  And he knew how much money and where it went (in the fuel tank, and not something else).   For all we know, this gal's story might have been on the up-and-up.

If in doubt, it is better to ere on the side of generosity.  And that is what Frank did here.