Not so. Generally, there are two types of preseason games. First, there are exhibition games, which can be played against D2 or D3 teams. Those exhibitions are allowed to have spectators and are played like a regular game. Normally exhibitions cannot be played between D1 teams. Secondly, there are scrimmages against D1 teams, which must be held in private and are not supposed to have any official statistics.
However, there is one exception to the rule about exhibition games. If two D1 teams get special permission from the NCAA to play a game for a special charity then they can play a game in front of spectators with a real score being kept etc. In the case of the South Carolina vs Rutgers game that you mention, it was being played to raise money for a specific breast cancer charity. Rutgers and South Carolina were granted a waiver by the NCAA to play this exhibition game in honor of Nikki McCray-Penson, who was an assistant coach on both teams and passed away this summer.
That game was not at all like the UConn exhibition game that will take place next Saturday.