Well, as someone who has a mildly life-threatening condition that manifested "off-book", and only one of several doctors I saw was able to identify it, I'm probably a bit more skeptical than average. But, it's worth noting that my symptoms were severe enough each time I had it that a PA would've certainly referred me to a doctor (I called an "advice nurse" each time who told me to see a doctor). So maybe that's a point in favor of PAs doing initial screens.
With respect to that comic, I would've gladly paid $4k out of pocket for a diagnosis. I still think fondly of the doctor who quickly figured out the puzzle that tricked a couple other specialists, my PCP, an urgent care doctor, and an emergency medical doctor. The same doctor who quickly sent me to the hospital in an ambulance with a note on my chart that said "this is serious, don't send him home until you confirm my diagnosis."
[1] http://extrafabulouscomics.com/comic/418/