Apparently they aren't checking men for "hemorrhoids". And checking for hemorrhoids or STD's was not given as a reason to do this.  

Somehow hundreds of police departments manage to do a pre-employment physical without this particular exam.  

Yes, it's a doctor who is doing this. And if he uses standard practices, there is a female nurse in the room observing, as a legal protection for him and for the patient. But there is no reason to do it, and it's not a matter of whether the doctor is comfortable or likely to be turned on or do something inappropriate.  It's a matter of whether it's relevant to the job.  It isn't.  And regardless of how many such exams a woman has, they are not something to be undergone for no good reason, by a doctor the woman did not choose.