> I can still license that code to a company and ask them to pay me for using the code
I believe you can do that with public domain/copyright free material in general. There is no requirement to tell someone that the material you license them is also available under a different one or that your license is not enforceable.
Depending on how you do it and they find out, you could certainly be sued for fraud and misrepresentation, though. And, if you put a "copyright by me" at the top of a public domain work, it's technically a crime under 17 U.S.C. § 506(c) - Fraudulent Copyright Notice
