Sounds like a BCS (body cavity search) isn't too far out of bounds for employers either. Its on their property right?
If you accept a job with the understanding that the employer retains the right to conduct a cavity search, then you are subject to cavity searches and may be fired if you refuse one.
The employer can't enforce a cavity search, and will be legally and financially liable for firing you if you refuse to allow them to conduct a cavity search, if you were never informed of the cavity search policy.
Is signed an agreement to submit to an employer-administered drug test at any time of their choosing. That's not much different than a BCS, IMO.