Yes they do, but they just get civil service salaries. The real payola is to run a private for profit entity that is contracted to provide services, and you will find the principal officers and owners are strong supporters of the continued candidacy of incumbent politicians who have some say over the whole monkey business.
Its what we do for business when real manufacturing jobs are done by cheap labor oversees.
I worked for a public employee union in California for years, and believe me, they are very well paid and retire better than most private workers.