this is all sounding very legal.
pre-employment medical exam. : the trouble is, this merely means, yes, give me a medical. It is just a formality - I still get a job even if I'm half dead. It's just that it comes before I start work, not a day or two after!
A pre-requisite medical examination to determine fitness for employment.
pre-requisite: a thing (here: the medical) that is required as a prior condition for something else (here: employment) to happen or exist