Interpreted tongues would not be a mystery. Although Paul could be simply referring to speaking in his native tongue quietly, there is no reason to assume this. It seems that Paul is allowing the person to continue speaking in tongues to God, but not in public address. Uninterpreted tongues may not profit the church, but they do profit the individual. I would conclude that uninterpreted tongues may be meaningless to other humans, but it is not meaningless to the individual speaking in tongues, nor are tongues meaningless to God who perfectly understands the language being spoken.
Uninterpreted tongues are permissible in the right context, and even encouraged.