If your main concern was acclimation to a full day schedule, there is no reason why a private pre-k couldn't accomplish this goal as well or better than a public one, even if the child will be going to a public kindergarten.
The point here is the bias of the reporter in calling public classes "pre-k", and private classes "day care". There are many fine pre-schools in the private sector, and they should be recognized as such in the press; that is, if they strive to be fair and balanced. :)
She did go to a private Pre-K. It was at the same school that she is going to now.