The coins in this case were stolen from the US Mint. They were never privately owned. http://en.wikipedia.org/wiki/1933_double_eagle
The original article is very misleading. It tries hard to make it sound like these were coins that the govt tried to confiscate from a private owner under the 1933 executive order, and that the govt never gave up on trying to seize that private property. That's not at all the case. The coins were stolen, and they're easily identified as the stolen coins because none of that date were released to the public.
It's analogous to someone finding the Gardner paintings, stolen more than 20 years ago, in their grandpa's basement. The statute of limitations has passed but the paintings are still stolen property, and still easily identified as stolen property, and if they turn up they'll go back to the original rightful owner, the Gardner museum.