This is true, that's how I'm getting therapy right now. I was scared this was too much paperwork for me at first, but my therapist explained that I basically needed to only do three things:

  (1) go to a GP (Hausarzt) and explain my situation so they fill up a report and confirm that the issue is indeed psychological and not physical,  

  (2) go to a therapist that works with public insurance so they can write another report, your therapist might refer you to one of his/her colleagues, and  

  (3) email five therapists that work with public insurance and ask them how long their waiting list is. They likely will all tell you it's longer than 3 months, which is what you need to hear.  

You basically send this stuff to your insurance company and they deal with the rest.