I don't know the exact legal situation in the US, but let me assure you, the described legal copyright situation is very much possible, because German copyright works exactly like that.
I am a software developer, so I write software. I am employed full-time by an employer for which I (usually) write code, documentation and such, and still I own the copyright to each and every line of code or documentation or whatever I write. Simply because copyright in German law is non-transferrable. Even if I want to, I cannot sign over the copyright to anybody else, hence my employer couldn't make me sign it over to him in my employment contract. Instead, there's a clause that I grant my employer an exclusive and irrevocable right to use the work I create during my paid work time in any way he wants. This effectively leaves me with the copyright, but I don't have any rights to profit off of that work anymore, so that copyright isn't of much use to me.
I am a software developer, so I write software. I am employed full-time by an employer for which I (usually) write code, documentation and such, and still I own the copyright to each and every line of code or documentation or whatever I write. Simply because copyright in German law is non-transferrable. Even if I want to, I cannot sign over the copyright to anybody else, hence my employer couldn't make me sign it over to him in my employment contract. Instead, there's a clause that I grant my employer an exclusive and irrevocable right to use the work I create during my paid work time in any way he wants. This effectively leaves me with the copyright, but I don't have any rights to profit off of that work anymore, so that copyright isn't of much use to me.