Answer
It executes as &AO (the application's own database/service account), not as the individual triggering user — so a user generally doesn't need direct database-level permission on whatever the SQL references, since &AO's own permissions are what's actually used to run the statements. That said, the triggering user's own language setting can still affect the event's behavior, since it can influence which localized value gets passed into any language-dependent parameters the SQL uses — so a user-specific issue triggering the same event can still occur, just via the parameter values passed in rather than a permissions gap on the SQL execution itself.