Yes, but as you note, the point is to make it sound like barely a confession, the minimum possible confession. This makes it just as attractive to the innocent as for the guilty. It's offering a minimally painful way out of a deeply stressful situation.

And as you say, the punchline is that not confessing would lead to minimal or no pain, and every level of confession will equally turn out much worse. An innocent person is just trying to escape from that room, and is being conned into agreeing to a long prison sentence in order to do it.