No. The law is very clear that you are allowed to make copies. For some time now you are not allowed anymore to circumvent copy protection for that, which is an illegal law but still standing, but even this is not happening here. The industry has no leg to stand on, this is just terror-by-suing, trying desperately to stiffle fundamental rights of german people.
I'm not defending the industry or the case at all. I'm just saying that saying "youtube-dl is technically a browser", and letting the defense rest its case, is the kind of technically-correct nonsense that often gets written on HN but would never work in the real world.
That's not nonsense, it's very relevant to this case and just the facts. That the judges in Hamburg are not suspectible to facts or reality is on them, not on HN.
And actually, it is what an expert courts should and do commission in such cases would explain.