1933 Double Eagle

After reading serveral articles on the material about the 10 rougue 1933 $20 Saint Gaudens Double Eagles that were found in a safety deposit box years after an alleged criminal passed away, it lead me to one question that I keep asking myself. Why did the heirs go to the US Mint to get them authenticated and why also did they leave the coins with the Mint, which for its part said "Thank you" and is keeping the coins that they claim were stolen (OK....improperly taken) in the first place. Needless to say, these folks are suing the Mint to get the coins back. Tune in to your favoite legal journal to see what happens next.

My question, and perhaps someone at NGC could opine here, is what if the family brought or sent the coins to NGC for authentication? Would NGC grade and authenticate them? Is there a secret handshake with the US Mint that mandates NGC (and other grading companies) to turn over the supposed contraband? Another question is how can the TPGs authenticate a coin that has not to my knowledge been authenticated by a TPG?

The way it looks now is that the US Mint is going to keep the coins and has made a decent legal argument that they are the US Mint's property.