Ooooops…. actually, I missed the point. The private posts do remain private, only, before that I was not able to see the private posts via the front-end, and could not preview them, except for the backend footer.
And now I can. I logged off, and the private posts vanished.
So, the upgrade (from 1.5.1 to 1.5.1.3, I guess) actually FIXED a previous problem, that I got so accustomed to…
Conside this problem solved.
