Answer: In this case, simply being assigned a school would not create McKinney-Vento school of origin rights, because the definition of school of origin is “the school that a child or youth attended when permanently housed, or the school in which the child or youth was last enrolled, including a preschool.” In the situation you described, the children never attended the school. Also, since “enrolled” is defined as attending classes and participating fully in school activities, the children really were not “enrolled”, either. If a student did not attend classes, the school to which they were assigned would not meet this definition.
If a homeless family became housed in the summer, they would have the right to school of origin for the following academic year (locally or state defined). McKinney-Vento does refer to “academic year” in establishing the right to school of origin if the child or youth becomes permanently housed in an academic year or over the summer. Whether a student remains in the school of origin depends on best interest factors. In the case of a family that is permanently housed in a new school district over the summer, those best interest factors may stack up in favor of enrolling in the local school for the new school year.