It's only the 1933 Double Eagles that get seized, and only because the government's position is those coins were never legally issued, meaning private possession of one could only have come about via theft from the Mint, which makes the coins stolen government property.
I think the previous poster was referring to executive order 6102 (April 5, 1933), which seized gold within the United States, and criminalized the possession of the specie.[1]
The number of exceptions in that order, and the fact that squads of government officials did not go door-to-door looking for unexempted hoards of coins, suggest that perhaps that order had more to do with PR than actual seizures.
