The short answer to your question must be:- "yes"!
It all depends upon the
environment it is being used in.

In the case you mention, don't forget that the rider in the gym is likely to be a fit, healthy person ... whilst the patient in physio may not be. In both cases, the folk in charge have a Duty of Care, but that should be a more onerous responsibility in the hospital setting.
Regarding the fan:-
everything within the patients' "clinical area" (or, if you like, reach) should be carefully used and correctly maintained ... otherwise they can become (literally) an accident waiting to happen. This is especially the case in places like ICU where the patient is already compromised.
The fan may not be a medical device
per se, but that won't stop it electrocuting the patient if electrically faulty (or indeed slicing off his fingers if he pokes them into the blades, or his ears if it topples onto his head)!

The seasoned biomed should always be alert to stuff like this, and act in a positive (and if need be, assertive) manner whenever s/he comes across it (as will no doubt happen from time to time).
Meanwhile, let's
link!