The Davis Square Community

Absolutely, it is a public school in that it is publicly financed. But it is not a public school in the sense of a public school district (which is the term I meant to use above rather than "public school.") For one thing, a true public school district has to take all comers - a charter school has an explicit cap on enrollment and therefore more certainty as to variable costs. In addition, students that require some special education services (not all, but some) are not allowed to enroll in the charter school and instead will be serviced by the public school district, at its expense.

Doesn't seem like a level playing field to me.