It has that in common with essentially all other open source license. And it only extends to the version given to you under the license. The copyright holder(s) retain the right to change their mind. Which is a reason AGPL v3 is popular with companies that are looking to sell commercial licenses for their software. There are quite a few startups out there that attempted to keep control whose primary business model is providing a way out from the many restrictions the AGPL v3 imposes on users by offering a commercial license.

In this case, it looks like Plane is not requiring copyright transfers. So that cuts off the practicality of them ever re-licensing their software (commercially or otherwise). That's a good thing as it means it is indeed not likely the license will ever change. The bad thing is that it would be hard to build a company around this project. The AGPLv3 is just very strict about having to open source any and all bundled features and imposes a lot of restrictions and requirements.