Ok. The def. says a condition wherein a patient believes he has one or more conditions that he does not have.
So Bob contemplates this . . . Hmm, what condition do I think I have that I really don't? Non-sensical.
There are steps that would be made, steps that are understood but outside the "scope of the puzzle." They involve cognition, action, and understanding by your imaginary players that MUST be considered or speculated upon if you even want people to respond. This is Wittgenstein's freed fly my friend. A positivistic display of logical equations doesn't come close to capturing the nuances involved with what a riddle conjures or the numerous modes of expressions and intentionalities in language that logic will ever fail to capture.
Now, back to the puzzle: As stated, hydrocondria requires an object other than itself, because if it is understood as being hypochondria, then it is also understood that the condition feared is non-existent and thus hypochondria is not in play. Unless of course you ARE the sort of person who fears everything about the world, including what is printed on a label or in a website, and too stupid or lazy to investigate what it means before whining to your doctor, in which case you are an idiot with anxiety issues . . . NOT a hypochondriac. As I stated.
We as literate human beings have a given understanding of certain terms and definitions. It goes without saying that hypochondria needs an object other than itself to be such. I understand you would like us to “bracket our learned understanding of this fact, but just because it isn't stated in the definition that Bob read, a definition that all of us, including your imaginary doctor, would know is pathetically vague, doesn't mean the doctor is in error. "He" would certainly have a better understanding of the matter than the web definition. Or do you have specific pre-fab puzzle parameters for your doctor's understanding of hypochondria as well?
Sure, if we stick to Bob's imaginary world and your hypochondria as defined, and assume the doctor goes by this fictitious understanding of hypochondria too, then ok, the doc is wrong. But what's the fun in that?