The largest part is syndication fees. You're seeing a pie chart about public radio station income, not NPR's income. See further down on the same page, in which it is indicated that 37% of unrestricted NPR income is from program syndication fees.

"Program fees and dues paid by our Member Stations are the largest portion of NPR's revenue. This includes fees paid to air the NPR newsmagazines, other programming we produce and distribute and annual member dues." and

17% from corporations, but also count foundations if you're looking for underwriters overall, not just corporate interests. Probably also universities and "other" for 41.6% That's still not even remotely close to a vast majority, of course. And I think there's a qualitative difference between getting funding from an organization that wants to increase its bottom line and one that wants to create a more just, verdant, and peaceful world.

17% is for member stations. In the NPR chart, corporate sponsorship is 25%. I'm not sure if this includes the 17% of 37% that they get from member stations, but I would assume that it does not, thus getting the amount of corporate money in NPR's own revenue to about 31%. Nowhere near vast majority still, even if we assume that "other revenues" and "grants and contributions" may have some corporate money too. I see no way it could be over half with any sane set of assumptions unless I'm completely misinterpreting the data in these diagrams.