A significant proportion of science research is funded by non-governmental organisations - for example the Gates Foundation.
Furthermore, most universities will charge the researchers who receive grants a cost known as 'overhead' that can often be 100% of the grant. Typically, the funding agencies pay for this separately.
When it comes to basic science, this is not true at all. Gleaning numbers from Wikipedia, the Gates Foundation seems to spend roughly $300 million a year on research. HHMI (Howard Hughes Medical Institute) spends $450 million a year. In contrast, the NIH spend $31 billion a year. Biology and medicine are the fields with the highest proportion of private funding, and even in these fields the government is dominant.
Overhead is relevant as it shows that even at 'public' universities, the funding agency must pay for the research to be carried out, countering arguments about the public paying for research.
Where it gets quantitative, the Wikipedia page seems to be talking about "R&D" in general, which is an accounting category that is much broader than "research". When Intel designs a new CPU or Boeing designs a new plane, for example, that's under the "research and development" rubric in these figures. But they typically don't publish much about it, and a lot of what they're doing doesn't have much to do with the kind of "research" we're talking about here.
Perhaps more relevant, though, very little research indeed is funded by subscription fees to scientific journals or conference proceedings or sales prices of academic books; journal and conference authors don't even get royalties, and neither do their institutions, and very few academic books make a substantial amount of money.
I don't understand why overhead is relevant; we're arguing about who the funding agency is, not how grants are structured. If the NIH has to spend 40% of their dollars on overhead so that their PIs have offices and library access, and so does the HHMI, how does knowing this allow us to more accurately compare the expenditures of the NIH and HHMI?
