I agree that fifteen minutes minus paperwork is shockingly short. Still, there are doctors who do reasonably well at paying attention.
Most of my information is from the fat acceptance community, where there are a great many stories about doctors who just tell fat patients to lose weight*, regardless of symptoms. The typical stories seem to be either "I had to go to three or four doctors to find one who would listen" or "I must be lucky, I have a great doctor". I can't derive a strong opinion about the proportion of attentive doctors from this, though I wouldn't be surprised to find that it's under half.
*I've also seen a few stories from unusually thin people who were simply told to gain weight, and one from a man who (as far as I could tell) was lean and muscular, but was told to lose weight by a doctor who literally only looked at his BMI.
International list of fat-friendly medical professionals
...A fat friendly professional does not necessarily avoid mentioning a client's weight, but he or she avoids making an issue of it, avoids lectures and humiliation, and respects the client's wishes with regard to weight discussions.
If a client asks not to be weighed, the request is acknowledged without complaint and taken into account automatically on future visits. (Note: there are a few cases where weighing is necessary, for example, when administering certain medications, chemotherapy, or anesthesia
In a world where 85% of doctors can't solve simple Bayesian word problems...
In a world where only 20.9% of reported results that a pharmaceutical company tries to investigate for development purposes, fully replicate...
In a world where "p-values" are anything the author wants them to be...
...and where there are all sorts of amazing technologies and techniques which nobody at your hospital has ever heard of...
...there's also MetaMed. Instead of just having “evidence-based medicine” in journals that doctors don't actually read, MetaMed will provide you with actual evidence-based healthcare. Their Chairman and CTO is Jaan Tallinn (cofounder of Skype, major funder of xrisk-related endeavors), one of their major VCs is Peter Thiel (major funder of MIRI), their management includes some names LWers will find familiar, and their researchers know math and stats and in many cases have also read LessWrong. If you have a sufficiently serious problem and can afford their service, MetaMed will (a) put someone on reading the relevant research literature who understands real statistics and can tell whether the paper is trustworthy; and (b) refer you to a cooperative doctor in their network who can carry out the therapies they find.
MetaMed was partially inspired by the case of a woman who had her fingertip chopped off, was told by the hospital that she was screwed, and then read through an awful lot of literature on her own until she found someone working on an advanced regenerative therapy that let her actually grow the fingertip back. The idea behind MetaMed isn't just that they will scour the literature to find how the best experimentally supported treatment differs from the average wisdom - people who regularly read LW will be aware that this is often a pretty large divergence - but that they will also look for this sort of very recent technology that most hospitals won't have heard about.
This is a new service and it has to interact with the existing medical system, so they are currently expensive, starting at $5,000 for a research report. (Keeping in mind that a basic report involves a lot of work by people who must be good at math.) If you have a sick friend who can afford it - especially if the regular system is failing them, and they want (or you want) their next step to be more science instead of "alternative medicine" or whatever - please do refer them to MetaMed immediately. We can’t all have nice things like this someday unless somebody pays for it while it’s still new and expensive. And the regular healthcare system really is bad enough at science (especially in the US, but science is difficult everywhere) that there's no point in condemning anyone to it when they can afford better.
I also got my hands on a copy of MetaMed's standard list of citations that they use to support points to reporters. What follows isn't nearly everything on MetaMed's list, just the items I found most interesting.
90% of preclinical cancer studies could not be replicated:
http://www.nature.com/nature/journal/v483/n7391/full/483531a.html