Define crappy. On initial hire they run an EKG to check for an irregular heart beat, check to see if your blood pressure is within a set normal range for your age, run a hearing, vision, color vision screen, check you for hernia and ask that you list all meds you're on and any major illnesses or inpatient hospitilizations. On the balance it isn't that bad. I've got 20/200 vision corrected to 20/20, which is the key. My blood pressure though, oh boy. A doctor/nurse takes it and it skyrockets. I was nervous on my initial hire medical. I take mine regularly since I have a family history, its high but within standard, 135/90 I THINK is standard (need to quit smoking). I see a white coat and it hits 160/110. The aviation medical examiners are good about knowing that 99% of the people they see are nervous. I had mine taken more than once on my initial hire.
The other medical thing is you would not believe the list of meds a controller cannot be on. If you're on one of them, no chance. I'm dating a nurse practitioner who when she saw the list (yes you cannot take benydryl) which is about 4 pages was absolutely speechless for the first and only time since I met her

I'd address any questions to the ask a medical examiner (never frequent it, sorry that I don't know the exact title) forum on this site.
As for the FBI thing. I guess it depends on what it is. If its funny I suppose it can be explained if needed. I wouldn't wory too much, its more about you.