Can hidden cards affect other battlefields where the showdown is happening, such as cards that draw or cards like Zhonya and Tide Turner?

Ruling: This question has been previously answered in another thread. The answer is available in a referenced discussion.

Nuances:

• You cannot target something on another battlefield
• The specific ruling for cards like Zhonya and Tide Turner that don't target but have effects (like draws) is addressed in the referenced thread