However, I don't know any good way to fix it. Hiring is a tough nut to crack. Clearly, one can always be more assiduous in following up references, but that's not always a big help, because you are then in the position of trusting what one stranger is saying about another stranger, in a situation where the motivations of the reference are not always clear.

Note that saying "Any other referral carries no weight and should be treated the same as any candidate off the street" doesn't solve the problem-- the "any candidate off the street" problem is the problem.