According to the President's Cup manual, "State Select/ODP/Challenge teams may not compete." MPSC 92 White should not be competing in the President's Medal Cup, but I guess it's up to SCYSA to make the final determination.
As far as classic teams go, the distinction between playing in division I or II for the regular season was made based on the coach's or club's assessment of the team before the start of the season. If a team was very successful during the season, it is only right that they participate in the higher division of the Cup.
Only the winners of Division I qualify for regional play next year. No reason to exclude a team because they underestimated themselves prior to the season, and now want to play at the correct level, whether that be moving up or moving down. The intent is to find the best team to represent SC at the regionals, and to have some parity in the tournament for the rest of the teams.
....I hope it is a typo