Those graphs don't really refute the point.
Look at the buckets: Things like Dental Services, Home Health Care, Nursing Care Facilities... This tells you about healthcare spending at the macro level, but doesn't explain why a particular doctor visit cost so much (I don't use any "nursing care facilities" or "dental services" when I visit the doctor for a sprained ankle, for example).
When you go to the doctor for a sprained ankle, where does that money go? By law, no more than 15% is going to the insurance company (which isn't just profit, that covers all the administrative costs of running the plan). Where does the other 85% go? Certainly some it is the cost of running a clinic (staff, rent, equipment, etc), but what about the rest?
Then look at doctor's income. Your basic family care provider living in Podunkville earns as much as a mid-career SWE in the Bay Area, and specialists earn way, way more. Where do you think that money comes from?