My stepfather went for a routine visit to the doctor in Vienna, Austria. They found a suspicious object, and decided to treat him immediately, and he was operated on the very next day. It ended up being benign, but I was amazed at their speed of treatment.
My uncle went for a cardiologist evaluation here in Montevideo, Uruguay (where we have a form of socialist-style medicine in the style called Mutualism). They found a suspicious spike in his heartbeat, which they suspected to be a treatable syndrome (Wolff-Parkinson-White), and decided to do some special evaluations. He was treated (with full anaesthetics) one week later (at almost zero cost).
Both were quite good experiences, times are a little slower in Uruguay but everybody has access to basic medicine.
That said, I suspect that for difficult-to-catch diseases, you have to make yourself a bother, otherwise you might slip through the cracks like your friend almost did (doctors here in Uruguay are heavily penalized if they take too much time with one patient).