Seems easy enough for the NIH to counter by changing their funding policy to exclude all "private sector research works", leaving academics and universities to decide whether they'd rather carry out research nominally under the auspices of some public sector organisation that handles distribution or not take the funds. If they really wanted to they could even introduce their own peer review process for final publications too...

It's remarkably short-sighted and pointless legislation, unless the real objective is to start suing authors for forwarding PDF copies of their work and related documents to interested parties without journal access.