Title says it - I need to get a notification when any card, on any board belonging to a given organization changes.
Webhooks on Organization (team) models only trigger when something directly connected to that team changes. For example, when a board is added to the team, or when the description of the team is updated.
If you want to watch for changes to any card within an organization, you will want to watch the organization, and any time a new board is added, you will want to add another webhook on the new board.
This should give you full coverage of the cards "belonging" to a team.