That's straight up not true. Most of the money spent on research is obtained directly through pharmaceutical sales in the US, and a large chunk of the rest is obtained indirectly in the same manner.
Medicine is perhaps the industry that most exemplifies one with large confluent streams of money from public, private, and charitable sources involved at different levels of training, research, and practice.
Yes, as someone who's actually done this sort of tracking and research extensively, it has, in fact, occurred to me that it is a complex task.