I can see that, but here's another hypothesis...
Students at private schools may have more financial pressure due to the extra tuition, so they need to have better grades to keep scholarships and graduate on time. Staying an extra semester or year at a school that charges $40k/year is more of a financial burden than one that charges $10k.
Of course I could also see the argument that stereotypically rich kids are more likely to go to private schools and thus don't have the financial burden, and those with less liquid assets go public because that's what they can afford. But that's the Libra in me
The data nerd in me, however, thinks we need more factors than just GPA vs. public/private.