I think that's a reasonable analogy but I draw the opposite conclusion from it. If you divide the world into alcoholics who need rehab and normal people who don't, you end up with a lot of people who refuse to admit they have a drinking problem because they don't want to pay the social costs of doing so.
Something many alcoholics and nearly all non-alcoholics have in common is they deny being alcoholics.
P(Alcoholism|Denial of Alcoholism) = P(Denial of Alcoholism|Alcoholism) * P(Alcoholism) / P(Denial of Alcoholism)
Pop in any reasonable numbers for those terms and it becomes readily apparent that denial of alcoholism does not constitute meaningful evidence of alcoholism.
