My guess is that Texas law gives the governor the power to modify the list of available vaccines given to school children. These sort of detailed items are usually not written into law but are under the authority of various agencies to administer.
That is interesting and I could see how that would be used to justify Perry's actions. However, it sounds very questionable because if the governor is actually writing and modifying the list of legally required vaccinations, he would be effectively legislating and changing Texas law. This violates the idea that the legislature cannot delegate its constitutional legislative powers to other entities without a constitutional amendment. A reasoning which I believe the Texas Supreme Court has been fond of in the past.