Taking emotion out of the equation and looking at the whole mess from just a strategic / analytical point of view. The dopes on the BOT made a humongous strategic error by firing Joe when they did and how they did because it more or less completed an admission of guilt. Even IF the BOT had evidence the C/S/S and Paterno were guilty and/or complicit, their #1 objective was to protect the interests of PSU. They needed to view every move, every press release, every sound-bite from the angle of "what is best for PSU .... what will make PSU look best in this nightmare".
A 1st-grader with a middle of the pack IQ could have realized that firing Joe was going to create a media frenzy and was going to create that admission of guilt. I am assuming that most members on the BOT at the time, were smarter than an average 1st-grader. What they could have done, was simply put Joe on administrative leave while they investigated the case. In other-words, they stall and delay. The stall and delay tactic is used time and time and time again because it is a fact that the media gets bored on a story, and they will eventually turn their focus to the 'next' story. At the time there were 3-games left in the season, they could have simple released a statement that because of the situation, they felt it would be in the best interests of the team and the university if Joe was placed on administrative leave.
This would have diffused the situation .... not ignited the situation. Instead, the unbelievable decision they made, definitely ignited the situation, and more or less spelled out in great big bold neon letters for everyone "WE ARE GUILTY".