TSA rifles through wallet, confiscates ID

I have always wondered when flying as a selectee (declining to show ID) if the TSA might rifle through my wallet and find my ID for themselves. We know that we consent to a search of our belongings when we enter the security line, and that there is no option for refusal. While we have learned that the TSA may record things like the books we read, I have always assumed that the search itself must be reasonable. However, Dmitry Samarov reports that the TSA rifled through his wallet, examined his ID, found one that was fake (although very old), called the local law enforcement, and confiscated it. I have previously pointed out another case where TSA agents rifled through a wallet and asked a lot of questions. Our right to fly without presenting papers thus may be limited by the TSA rifling through our things to verify our identity. What are our rights when travelling?