Woody said he was "hired on as a camera man's helper", during the BPA project - so if the US Government wasn't paying him to write the songs, they wouldn't own the rights to them.
But I think the idea of anyone owning the rights to a song after the person who wrote them is dead - apart maybe from while the children are growing up, or during the lifetime of the wife or husband - seems pretty sick to me. And I'd adduce Woody in support of that view:
Was a great high wall there that tried to stop me;
Was a great high sign there says "Private Prop'ty."
But on the other side, it didn't say nothin' -
That side was made for you and me.