What EventBridge gets from CloudTrail?

That's correct: CloudTrail events that are captured by any of your configured trails in the region are delivered to EventBridge, and events not recorded by any of the trails you've configured do not get delivered. It's summarised in this documentation segment: https://docs.aws.amazon.com/awscloudtrail/latest/userguide/cloudtrail-aws-service-specific-topics.html#cloudtrail-aws-service-specific-topics-eventbridge

The point about some events being reported both by CloudTrail and the underlying service refers to that information about certain types of events is available directly from the underlying service as well as by listening to CloudTrail events. For example, if an EC2 instance is stopped by the customer calling the StopInstances API, it can be observed either by listening to CloudTrail for that API call or by using the EC2 instance state change notification that EC2 delivers to EventBridge without involving CloudTrail: https://docs.aws.amazon.com/AWSEC2/latest/UserGuide/monitoring-instance-state-changes.html.

However, while both methods would detect an operator shutting down an instance, the event from EC2 wouldn't say which IAM role or user requested it, while the CloudTrail event would contain that information. On the other hand, the EC2 instance state notification would also respond to an AWS-initiated event or hardware failure, while CloudTrail would only log events requested explicitly by calling an API in your account.