That is a clear misinterpretation of the law. The law says that copyright protections do not exist for government work created for a government capacity except where noted. That does not mean any of that work is in the public domain. Just because copyright protections are not available does not mean other intellectual property protections are equally void.

Here is the law text: https://www.law.cornell.edu/uscode/text/17/105

By the way it seems most of the stuff I produce for the government contains copyright notices. I don't know if those notices are valid or not, but none of the stuff I produce is in the public domain or released to the public.