Blue skin is a symptom, not a diagnosis. I doubt the doctor who saw him could immediately diagnose it, however he didn’t give up and cracked that case eventually (and even found the cure!)
The doctor would have to do a bit of research, but being such a rare symptom, achieving a diagnosis for blue skin would be much easier than reaching a single diagnosis from something like chest pain.
It's a lot easier to treat someone when you can diagnose them at a glance.