For regulated industries that are required to monitor employee electronic communications, there are laws in place that prohibit companies from monitoring employees if the employee has a reasonable expectation of privacy. By having a company sanctioned social tool with a group type of Private or Secret, you may be giving the employee leverage to argue that the company can not use anything they post in those groups against them. This might include violated corporate policies, HR issues/inappropriate posts, or even illegal activities). See the blog post Private and Secret Groups - Legal Issues with the Terms for a deeper dive into this topic.
This idea is requesting that a future Jive product implementation change the names. We have changed the names to "invitation only" and "unlisted" to avoid this potential legal issue.