First of all, that's a far nicer looking piece of kit than the one I had imagined.
No doubt the manufacturer's label (partly obscured in the first image) says all the right things. Any chance of posting a picture clearly showing the label? Also, what (if anything) does the manual have to say? Any declarations about electrical safety?
The second picture shows what appears to be a white mains cable coming into the box. Is that a Y-split? If so, what is that all about? Is the cable detachable at the box end? I'm guessing the the red and black leads are part of your test kit!
So, the screws you mention are earthed. So that must be where you poke the tester probe, then. I assume that the black foot control is for the 'scope (and camera?). That connecting cable doesn't look very robust. Best get a spare in stock straight away!
Meanwhile, what else is in that medical room? Is the chair earthed? What's that other kit? ESU's? Suction? Any equipotential studs on the wall(s)? Any anti-static wheels, tubing etc. in evidence?
Lastly, consider how things will be there in a few year's time. Think fluids, rust, scratched paintwork etc., etc. As I have hinted at before, personally I would like to have "everything" in there to be at the same potential. That is, earthed.