It seems like classifications differ between regions. In the US, an illness is rare if it affects fewer than 200,000 Americans. In the EU it’s less than 1 in 2000 (or less than 0.05%).
No cure, blood test, or scan usually means its not a clearly defined illness, just a symptom. You don’t say someone having a heart attack and someone shot in the chest have the same syndrome just because they both have chest pain.
There’s a whole bunch of autoimmune diseases that have no cure, no specific blood test and no specific scan to diagnose them - but they are illnesses/diseases. Lupus is just one of them.
They are described as that but that doesn’t make it particularly scientific, or at least how most people define it.
I’m not saying all illnesses with no cure, blood test, or scan are inaccurately described or diagnosed, but I am saying it’s a pretty good sign. I experience pretty bad Raynaud’s(doctors thought it could’ve been Lupus but I don’t have other symptoms) but that isn’t enough information to describe an illness, because there are many things that could cause that- describing a symptom or group of symptoms as an illness implies there’s some sort of common cause and treatment, other than just treating the symptoms. Until that is found you can’t really know it’s a shared illness, just a shared symptom.