This is strikingly similar to the best argument I could come up with about why people are jailed for vice-crimes. If the state allowed people who were known to be drug users to have freedom, the populous would catch on that the State's laws against the use were hurting people that could be productive and were perpetuating real crime by shoving the behavior into the black market. The only threat they pose by being free is to the state's legitimacy.
So here, the only justification for these searches, these invasions of persons and property, is that if these people were able to escape the scans and gropes they would show that the prohibitions on fingernail clippers, full sized shampoo, and lighters were meaningless.
The legitimacy of the state must not be questioned, and the state will take any measure against its own people to ensure that the bulk of the population doesn't catch on to its lack thereof.