You can do something very simple like having a system that just lists if a person is - at that moment - in government custody. After release, there need not be an open record since the need to show if that person is currently in custody is over.
As an aside, the past few months have proven that the US government very much does not respect that reasoning. There are countless stories of people being taken and driven around for hours and questioned with no public paper trail at all.
Democrats love it too.
They call em Jump Outs. Historically the so called constitution has been worth less than craft paper. From FDRs executive order 9066 to today, you have no rights.