Yeah I think the context matters a lot there. I’m assuming it means “on a state by state basis”, which is true. But within my state, at least, family income, outside spending, and property tax revenues correlate very strongly with outcomes.
I've seen that too, but to my understanding it is less about the money and more about the parent participation. Wealthy school districts don't have any problem with finding volunteers for all sorts of activities, because one of the parents is frequently a stay-at-home parent.
This is true, but it’s also true that the money buys all of those extra activities and services. At my kids’ school, the garden program, music program, arts program, and teachers aides are all funded by the PTA. The field trips are funded by the students families so must be calibrated to their budgets. There are also volunteers associated with all of those programs, but they wouldn’t exist without the money.
A few (much wealthier) towns over, the district wide PTA raises millions of dollars yearly to support additional programs and facilities, and the district can offer higher salaries because of the larger tax base. Again, lots of parent involvement, but there’s also more to be involved in.