Can you gain a conquest point for winning a showdown at a battlefield on your opponent's turn?

Ruling: Yes, you can score 1 point for conquering a battlefield on your opponent's turn if you win the showdown there.

Nuances:

• You can score 1 point per battlefield per turn, regardless of whose turn it is
• This applies when your unit is moved into a battlefield on your opponent's turn (e.g., via Charm) and you win the resulting showdown