PBS & the National Academy of Sciences: Slighting Taxpayer Largesse

WillyShake over at Unconsidered Trifles notes some PBS deceit:
"When public broadcasting’s integrity is attacked, the PBSers harrumph that government money is only a tiny fraction of their budgets. But, they say without taking a breath, if you take even one penny of it away, it will destroy us.

And on one of the National Academy of Sciences FAQ pages:

Q: What is the relationship of the National Academies to the government?

Answer: "The National Academy of Sciences was created by the federal government to be an adviser on scientific and technological matters. However, the Academy and its associated organizations are private, not governmental, organizations and do not receive direct federal appropriations for their work. "

but, further down...

Q: What is the Research Council's major source of funding?

Answer: "The federal government funds about 85 percent of the institution's work."

What is going on here? Both organizations were founded and generally operated with good intentions. They have since been politicized by the liberal LAWYER and EDUCATIONAL establishments, respectively and both now engage in self-serving doublespeak given above.
I have been supportive of PBS, although the chronic, unbalanced propaganda of lawyer proxy, Bill Moyers was sickening and anything but educational. PBS gets too many of my tax dollars and it looks as if NAS does, too, admittedly or not.