The difference between a trained lawyer or accountant and someone with a lot of exposure to such knowledge is very specific skills and procedures. The difference between someone who is a trained manager with a degree and someone who's managed a medium sized organization is more or less nothing just an ability to use jargon.
I've actually looked online courses and documentation on epidemiology and public health. Unlike medicine (which I know nothing of) or advance mathematics (which I know and I know it take specialized skills), epidemiology seems to be a "smattering" sort of fields. A mix of public policy, simple medicine, biology and experimental methods and statistics. I could be wrong but it seems a field that's wide, not deep.
As far as I can tell, the person who actually leads the Gates Foundation health division is Trevor Mundel. Even then, the work of the Gates Foundation has been in funding projects lead by other organisations, rather than in implementing those projects themselves.
If they do it very well and can point to measurable results of success, I would think so!
His work in eradicating Polio. Choosing which projects to finance is a skill in itself, something he's likely more capable of than a traditionally credentialed expert. I can't help but think that you have an arbitrarily narrow definition of expertise.
There is no basis at all for claiming he’s a public health expert. He might be an effective philanthropist, but that’s a completely different topic.
You’d presume he’s learned a fair amount about it over the years. But I’ve learned a fair amount about accountancy through my years of working with corporate accountants. I’m definitely not an accountancy expert though.
What qualifications do you imagine he has? What significant work do you believe he has personally contributed to?