“Funded by a private corporation funded by the American people” is just a euphemism for state funding; the oddness of the euphemism is explained by the fact that it’s a euphemism in the first place.
What baffled me was - why on earth would you just come out and say that? It's kind of hamfisted and not entirely true either (the CPB had a board with members nominated by the President, amongst other government officials, although it's technically true that the CPB is a private institution, much like the Federal Reserve).
I was directly replying to the comment above me about the oddness of the CPB interstitial by providing an explanation. That might have been tangential but it wasn't off-topic. You're the one having a failure of understanding here, even though I've been patient with you and tried to explain the relevance of my reply.