If you guys aren't seeing a closed pit until the field has bunched up behind the safety car then it probably means the stock car rules aren't being used. There are two things you have to do to run a stock car rules server:
1. Enable the stockcarrules.dll plugin on the server. When setting up the server you can just load the sim in single-player mode, go to Options/Plugins and make sure it's turned on, then exit.
2. Include the NSCRS15.rFM file in the vMOD. See link and info on this page:
http://rfactor.net/web/2015/09/25/2015-stock-cars-now-available/
If you want to use the NASCAR-style knockout qualifying then that's a separate plugin that has to be enabled in the same fashion, called KnockoutQualifying.dll.
As for private vs public qualifying, the point of knockout qualifying being used in real life is that outside of restrictor plate tracks (in rF2's case, Jacksonville and Alabama), all cars start out the qualifying session on track together rather than how they used to do it, which was single-car qualifying (private, essentially). Knockout format is used so that the very top grid positions will be less affected by traffic impacting lap times.
So basically if you use knockout style, it makes sense to leave it public, but if you want single-car qualifying then you should run private and leave knockout qualifying off.