A "Strong Indication of an Illness" Should NOT Mean "No Illness"

I think it's put it in there to make you work for a diagnosis and go that extra mile and not just have an open and shut case. It's just trying to simulate the medical process and that isn't always cut and dried. I'd be disappointed personally if everything was very easy, and your diagnosis was super sure without work.
In real life medicine there are tests that come back that indicates an illness. Elevated white blood cell count is one of those. So your doctor usually does more workup if your test comes back showing this. There are reasons other than illness that you could have an elevated WBC also. Things like.. medicines you might be taking, stress, allergies, pregnancy.. ect.
Now the sims is not of course like normal medicine it's silly and over the top and not anywhere near as gritty lol. When I have my sim treat another sim I usually keep my camera on the patient, swinging back to observe them often. I watch their symptoms or watch for none during the testing work up. That is pretty much the only way I can narrow down the possibilities other than through testing. Carl's has a good guide on what all the circles, lines, heat, stars, sneezes ect could mean. Sometimes I use that as a cheat sheet if I'm playing a good practitioner. Sometimes I just guess if I want my sim to fail..
If I have any real beef with this system it's the grind. Funny thing is I don't mind the grind in the other careers. Probably because they get out more often early in the career ranks. I usually have to rotate to another house to get a break if I'm wanting a sim to get ahead in the medical career.

Yeah, it's true that sometimes they really do make you work for an accurate diagnosis. There are times where the patient in question is stubborn and shows no symptoms whatsoever, and yet the guaranteed diagnosis confirms that they do actually have an illness. At least when I have a hunch that they aren't sick, though, the "no illness" diagnosis has no negative effects on work performance if it happens to be wrong.