I've never heard anyone ever report that NPR has answered to the Federal government in any manner regarding their reporting.
How much are they willing to bite the hand that feeds them. It might be a small percentage but it makes part of their budget.
I see strings: the government wants you to buy a house, buy an electric car, and give to charity. You can't claim those tax deductions and credits until you've done those things.
But the crux of the issue is the question "does a small amount of federal money influence NPR". I think the answer is "it does not". I've listened to NPR and read NYT, WSJ, WashPo for years and I've never heard a peep about the federal money influencing NPR.
The OP is stating there are strings attached and NPR answers to the Feds. I've never seen one iota of that in my entire life.