A corporate car, which is given for personal use, is also still considered corporate property and the person using it, at some capacity uses it for work related purposes.
This bill says, if teacher X decides to protest, no matter if on school property or at a public park, they better be sure not to use that vehicle or they are in violation of the law. Not that a school district would EVER give a teacher a car. But superintendents might, and some superintendents are disgusted with the legislation in Arizona as it pertains to education.