This question is prompted by a couple of answers I've given recently.
This one, which really sounds like a 5 year-old with OCD.
This one, where one possible explanation is face-blindness.
In both cases the OP was not asking for medical advice; the questions were about worrying behaviour. In theory such questions might arise about physical conditions too, but with those its much more likely to be seen as a medical issue by the parents.
In the second case @Joe criticised the answer:
The "WebMD" syndrome, where people look at WebMD for "what is symptom X" and see "x cancer" or whatever and the other long list of bad things it could be, when it's probably just a stomach ache; thus causing lots of needless anxiety.
Joe is certainly right to be concerned about this (which is not a new problem incidentally; Three Men in a Boat from 1889 includes an anecdote about the narrator's encounter with a medical dictionary). The Internet is full of misinformation about medical matters and we should certainly be cautious about adding to it. However we should also beware of withholding information because we fear what the recipients might do with it. Despite the large amounts of idiocy in the world, I cling to a belief that more knowledge is better than less.
Hence I would argue that such answers should be acceptable as long as they:
emphasise that this is not a medical diagnosis, rather it is a possibility that the parents might want to consider and research.
say that if the parents are concerned then they should seek proper medical help.
This SE is meant to be a resource providing useful information to parents. The fact that a particular pattern of behaviour matches, or might match, the symptoms of a known psychological issue can be important information. In both of these cases I decided to make a suggestion on those grounds. In one case I got voted up, in the other case down.
I considered just saying "see a doctor". However that would not have been useful in the faceblindness case because even today many doctors have not heard of it. Personal anecdote here: I have mild dyspraxia, which my mother picked up on when I was at primary school. I remember very clearly the doctor's appointment; he walked me up and down a corridor and then told my mother there was nothing wrong with me. Dyspraxia, of course, was not recognised in those days. Even "clumsy child syndrome" was another decade or two in the future.
This leads to another issue with such questions: the frame "medical issue" is actually pretty fuzzy around the edges. There are an increasing number of issues which were once considered behavioural or moral, but which have now been shifted into psychology (e.g. ADHD, dyspraxia, overeating), and others which have been shifted out (e.g. homosexuality). If "medical issue" is in part a social construct then its probably not a solid ground for a rule here.
So my question is: how should one proceed when a question makes one think "That sounds awfully like X Syndrome"? How certain should one be (given zero medical qualifications) before posting such a reply?