These two things were unrelated. It was actually the Somerset superintendent who was pushing for the public/private split, not the AD, and he was pushing for this before the two met in the 2005 semifinals. It was his own sentiment, not that of most of the Somerset fans. Any logical person can see that there simply aren't enough private schools in Kentucky for them to split.
To answer your question, I do feel like composure and discipline has been a problem for a few of the Somerset teams in the past few years.
2009 finals, PT might have been better but not 21 points better. I think Somerset had something like 8 turnovers in that game, one of which was a pick 6 on the opening play from scrimmage.
2010 semifinals, not trying to offend the Belfry faithful but you will never convince me that that Belfry team was better than Somerset that year. We racked up several penalties (deserved), starting RB gets kicked (also deserved), plus our best player being out for the first half after an appendix surgery and we all know the result.
2011, again from what I saw Holy Cross was probably the better team but not 28 points better. The first half the Jumpers were playing well and definitely looked like they were heading for the rematch with Glasgow, second half the wheels fell off and the unsportsmanlike penalties stacked up.
Just my opinion, but I definitely think that discipline has been an issue with some of the more recent Somerset teams. It seems like Lucas is taking the right steps forward to right the ship but I certainly think that these issues played a part in keeping us from getting over the hump.