Lie or Mistake?

[sanantone]

According to this site, they do all of those things.
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That being said, a county school board would be involved with most of the issues you mentioned, including budgets.  They would be responsible for oversight of the county school system, and in the case of Montgomery county, 20 different elementary, middle and high schools (if Wikipedia is correct).

strange 
I'm going to have to research my childhood county 

I know we had 3 incorporated towns and at least 3 non-incorporated "towns" 
our "big 3" each had their own police and fire department and each had its own elementary, middle and high school 

we didn't have a county tax, just a town sales tax  
I have no idea if the other towns had a sales tax or not 

I just can't see it making sense that a county school board would set budgets for towns of 5k people when the towns are miles apart from each other 
and the only thing the towns remotely have in common is the football schedule LOL

 

In Texas, school boards represent school districts. Some cities have many school districts. Some cities have a consolidated school district. Some counties have a consolidated school district. Hays County has a school district, but it only covers the areas not covered by the San Marcos Independent School District. San Marcos is the biggest city in Hays County.

Here in CA, school boards also represent school districts, similar to Texas from what it sounds.  School costs are paid for here by property taxes, not sales taxes.  That is why crappy areas have crappy schools, and nice areas have nice schools.  Completely unfair, and I have advocated a better system for years.  Why should you get to go to a nicer school entirely based on how much money your parents make?

Our schools are also paid for by property taxes. To try to make up for the disparity in home values and to respond to the school finance system being ruled unconstitutional, our state created the Robin Hood plan. The state takes money from the wealthier districts and distributes it to poorer districts. This hasn't worked out well either because this is also unconstitutional. The Texas constitution doesn't allow for a state property tax; property taxes are to only be collected locally. However, the Texas Supreme Court said that the current school finance system is constitutional, albeit, awful. It places a heavy burden on local governments because there is a limit to how much they can tax properties, and high property taxes are a pain for property owners.