Anyway, to continue the discussion...
Are you sure it's not one per player?
Other cards in the game specify when it's once across the entire group.
Yes. Read p. 14 of the Rules Reference - Limits and Maximums. "Max [X] per [period]" says for all players. It uses the "Max 1 committed per skill test" as an example even.
The restriction is the skill test. Any player is still playing into that specific skill test, regardless if they are active player or not.