When my Ping transaction fails, why does it still have a green icon in Manage Monitoring?

The Manage Monitoring display shows that status of collections, not the results of those collections. Since the Statistics Server is successfully running the "Ping", "PingCritical", etc. test, the icon is still green, because you're able to run the transaction test. Any failures for transactions will create Longitude events, and these events can be viewed in the Event Monitor.