Doctors here in Europe are not really into diagnostic medicine. I'm going to compare with Dr. House from the TV series who with a team spent days on a single patient. This is not the reality, the reality is that your specialist doctor will spend 10 minutes thinking about your case before moving on to the next patient.
I'm pretty sure that's not the reality... anywhere. That's TV.
10 minutes is extremely charitable. Make it more like 2 minutes. (And we give the government over half our salary for this level of attention!)
Keep in mind that even in the excellent documentary to which you refer, about Dr Hugh "House" Laurie, MD. PhD. McT., the premise is that his setup - a dedicated diagnostics team to focus on difficult to diagnose cases - is a rare concept, not something seen at most US hospitals. There wasn't, for example, a similar team in that other great documentary "Scrubs".