It absolutely does give a right to 'dictate', encapsulated in the dictum 'no taxation without representation'.
That is the whole basis of independent school districts local control is preserved and it is why residential segregation in the US works to maintain relative educational advantage and disadvantage.
Those school districts whose residents 'pay in' with large annual property tax cheques receive a 'payoff' in the form of excellent teachers, excellent sports facilities, excellent extracurricular activities, schools with great and well earned reputations, and property values that are maintained. This is accomplished via keeping the pressure on the elected officials (superintendents) and elected school boards, who run the districts and are responsive to the interests of the residents. Wealthier districts tend to have residents who have money to put where their mouth is.
Those districts whose residents are unwilling /unable to pay for excellent schools get mediocre schools. Residents in those districts also elect their superintendents and their school boards, but these bodies represent what the communities aspire to and find reasonable to expect from their schools.
In the US there tends to be a direct correlation between average property value and income, and quality of public schools.
Students report home that their university freshman year biology courses were a breeze thanks to the excellent teacher they had when they were 14." Doesn't say much about the course content at US universities at undergraduate level does it?
You are wrong to extrapolate in the direction you have gone there. It reflects in the case of my DCs' high school a biology teacher with a PhD from an Ivy League university who could easily have taught at a university but for reasons that are not clear (perhaps a guaranteed job and excellent pension?) chose to spend thirty five years teaching biology in a suburban American high school instead.
World rankings of universities are based on all sorts of criteria. Some place great store in them and some do not. It remains that some universities are extremely selective, by which is meant they admit under about 15% of undergrad applicants. Admission rates like that mean they pick only the best undergrad prospects America and the world can throw at them.