The fact of the matter is, once a card is added to your hand, it becomes your hand.
The difference here, both players know what the card is, and it isnt a matter of either player making the call here. The Graveyard has been altered and the only remedy is a Procedural Error Warning to be issued to the player controlling the effect, and possibly a Game Loss, as there is no way to verify the correct placement of
Snatch Steal back in the Graveyard.
More than likely, it would go as a Warning at a Tournament depending on the experience of the player. A table 200 player would probably get a warning, while a table 10 player could see a game loss since they really should know how to play at a more advanced level.
Casual Play is another thing altogether as there are so many different ways a casual game can be played. Some people use Japanese Cards or even God Cards. How can you "officiate" with an iron fist, a game that by UDE standards, may already be illegal?
The best you can hope for in a Casual Play Match is to correct bad play and move on.