If I play a Bone Skewer and, due to the effect, play Thousand Tailed from the opponent's hand onto the field, do my units receive the -3 penalty or do my opponent's units receive it?

When the opponent's Thousand-Tailed Watcher enters the battlefield via Bone Skewer, its triggered ability ("When you play me, give enemy units -3 might this turn") will affect your units.

Here is the breakdown of why this happens:

1. Controller vs. Owner: When Bone Skewer forces an opponent to play a unit from their hand, that unit is played under the opponent's control. Even though you are the one choosing the battlefield and forcing the play, the opponent remains the controller of the unit that enters.
2. Referencing "Enemy": As per Rule 359.3.f.4, terms like "enemy" and "friendly" in a triggered ability are checked from the perspective of the controller of that ability (in this case, your opponent).
3. Application: Because your units are the units controlled by the opponent's opponent, they are considered "enemy units" to the Thousand-Tailed Watcher. Therefore, your units will receive the -3 Might penalty.

This is an interpretation based on the standard rules for triggered abilities and controller references. While no official FAQ exists for this exact scenario, it follows the established mechanics for how "enemy" and "friendly" are evaluated relative to a unit's controller.