Can Shen be played as a Reaction to a Showdown triggered by an opponent entering an Open Battlefield that the player does not control?

Ruling: No, you cannot play Shen as a Reaction to a Showdown on a Battlefield you don't control.

Nuances:

• Shen's card text specifies that you can only play him to a Battlefield that you control
• Even without that specific text, the general rule prohibits playing units to Battlefields you don't control