I have now encountered six silver chests and have successfully opened each one. One thing I've noticed and I'm still testing is that you seem to get a treasure card any time you complete the puzzle without uncovering the X piece. Four of my games I didn't uncover all pieces (and lucked out without uncovering the X piece) and all four times I got treasure cards. The two times I uncovered all pieces I failed to get a treasure card. Not sure if it's the X piece, uncovering all pieces or something else that determines if you get a card or not; but I thought I'd just throw this out there for anyone who's interested.
Edit: updated counts on silver chests since my last post.
Thanks for sharing. I've never noticed that before your post. I also noticed a decline in silver chests since Marleybone. Mooshu and DS do not have as many or not at all???