Appearing before City Council for another day of grilling on the Philadelphia School District’s budget and proposals to transform operations and close dozens of schools, officials Tuesday said there were widespread misunderstandings about a plan to revamp the district. “Achievement networks” — groups of 20 to 25 schools run either by district staff or by outside nonprofit providers, such as universities or charter organizations — would be the foundation of the plan to decentralize. Those networks’ primary purpose would be to provide services requested by individual schools, School Reform Commission Chairman Pedro Ramos said.