No, I wouldn't say total slack definition is not true if you have SS links. I would say that start to start links mean that the finish of the task in question has no impact on the end date of the project, unless the finish extends past the latest date.

You need to review the logic in your project and determine what are the correct link types for each relationship. Tasks without successor or tasks with only a SS link imply that the finish of that task will not affect any other task in the project.