This statement is not true. It is the case though that many if not most public German universities have costs that run in the very low thousands i.e. 1-5k for total degree costs.
However, there are some drawbacks to the way this system works. For one, you will be hard pressed to find online degree offerings or continuing studies options from public Universities (i.e. these types of low costs offerings) that allow you to continue your education while working fulltime. Most of these come from private institutions or specific programs which have higher costs typically running in the 10k+ cost range area.
Its great if you are a student graduating from high school and going to university - you won't be burdened with high costs. However, the public system largely still neglects (this lone University being the only example in all of Germany which I am aware of) many other situations where people might want to further their education.
We do have something called Volkshochschulen, which is in some ways similar to Junior Colleges in the United States and provides some level of extended studies at a public level, but anyway, I won't go into details, suffice it to say the systems don't translate one-to-one onto each other and there are cons with our system as well.