Does state tax laws override school tax laws? (In Texas)?

We live in a county where if you have a new vehicle, you have to pay a school tax on your vehicle. My husband will use this vehicle for work, and according to the Texas state law (Sec 11.254) you are exempt from taxation if you use your vehicle for work. When he talked to you the lady about petitioning this, she said school tax is different and basically they can still tax us. Can anyone show me a law where is proves her statement or ours? I'm meeting with them and need evidence to prove my case. Thank you so much!