As far as I know, PUBLIC confession in the worship service (as opposed to private confession to a priest, who alone supposedly can grant absolution) IS a long time part of Calvinist worship, and completely in line with the Regulative Principle. No one is saying that the Church is granting absolution, rather that forgiveness is given by God alone. In the conservative Presbyterian churches I've attended corporate confession as part of the worship service is not unusual at all.
As to the RP: "Therefore, confess your sins to one another and pray for one another, that you may be healed." (James 5:16a (ESV))
One more thing: Calvin was fine about celebrating the parts of the Church calender that directly had to do with Jesus (Christmas, Easter, Ascension, Pentecost) just wanting to dump all the extraneous Saint's holidays the Roman church had added--saying they took the focus off of Christ. It was the Puritans, along with their stern version of the regulative principle (not practiced by Calvin) who banned all Christian holidays, including Christmas and Easter, and of course, Lent too.
Personally, I like Calvin better than the Puritans...