“Can be” and “are” are separate concepts. I know several of the teachers at my secondary school were grateful to live well outside the catchment area for students of the school. Being able to go out for drinks or dinner and rarely if ever see students is bliss. The school I teach at certainly is not meaningfully part of any neighborhood community.
Even the idea that teachers, administration and students are part of the same community is pushing the concept, unless prison guards and wardens are part of the same community as the prisoners.
This is like saying "don't you think the police are part of the community?" They are, but not in the sense of the community that should be the way kids learn how to be adults.
Do you think the schools and the teachers aren't a part of the community?