Gazebo only tries to download models it is going to use on the world being loaded.

Sometimes that message can be misleading though. If Gazebo doesn't find a certain model on your local paths, it tries to look for them online for a long time until it finally decides that the model can't be found.

This issue is relevant, it is about reporting the name of the model Gazebo is currently looking for.

Feel free to ticket an issue about disabling the download from database completely.