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I don't think there was a way for the public health authorities to create an explicit rule about neighborhood residency without inviting lawsuits. The best they could do is place vaccination centers in more convenient locations for underserved communities, and hope that it could raise the rate of vaccination in the vicinity.
I think there were people assuming that if it wasn't against the explicit rules to commute there to be vaccinated, it must be OK, even though it might (in the event of limited supply) undermine the effort to raise vaccination rates in that specific area.