Uh, no they don't. I'll try to explain with numbers; not the actual numbers but for the purposes of trying to get through to you what's happening, they're good enough.
Pre-charter: public school overall average = 75%
Charter school comes in. Give us your best students. We don't want the special ed students.
Charter average: 80%
Public school average drops to 65%. See how much better the charter school is doing? However, if you look at the average of those students pre-charter school, the students they siphoned off used to have an 85% average. And, in many cases, there's a lot more grade inflation in charter schools.
Clue: why don't you think there's a charter school whose mission it is to take the special ed students and all the other academically challenged students, and educate them?
You have to apply to get into charter schools. By default, that eliminates the kids whose parents don't give a shit about their educations. So, of course they end up with better students, on average, than public schools. That gives a false illusion that they're doing better.