appvol (great picture of UT by the way!)...admission to charter schools in NC is based on a lottery system (so there is no requirement for IQ testing, interviewing, income levels, etc.). Typically, during the first few years of opening, there will be more open positions than applicants, especially in the older grades. However, over time, the positions fill up quickly and the lottery becomes the primary tool for admitting new students. If your child does not get selected in the lottery, then you wait another year to reapply. There are some long waiting lists at most charter schools in the state.
When you mentioned prep (basketball) schools, I assume you are talking about Winston Salem Prep (dominant basketball program at 1A level right now). Winston Salem Prep is actually a magnet school under the control of the Forsyth County School system. I believe they have some sort of admissions process (interview, commitment of parents/guardians, etc.) but I know the school has been struggling academically (received an "F" on the NC Report Cards).
Sounds like your wife is at a very impressive school! However, it would not classify as a charter school in NC since admission is not by lottery (as required by the NC Board of Education and state law).
Hope this is helpful!