Each time a deployment project is created, all Bamboo users are unconditionally granted VIEW permission to the new entity. There is no way to opt out of this behaviour. The only workaround is to change permissions after the deployment project is created (after it had been visible to everyone for some time).
When creating plans and projects, on the other hand, there's a checkbox present which allows to control this behaviour. When enabled, all users will be granted the VIEW permissions. When disabled, no users apart from the creator will have any permissions. By default the checkbox is not set, making it an opt-in setting to make the new plan/project public.
Similar checkbox should be added for deployment project creation wizard, to allow creation of deployment project without having to worry about compromising potentially sensitive information.