The legal basis is explained here [0] . Funny thing is that in contrast to what the OP says the German net agency says that the CUII needs a court decision:

>A rights holder represented in the CUII can find copyright infringements and then file a lawsuit with the court for the implementation of a DNS block. If the court decides that a DNS block is lawful, this block is implemented by the Internet access providers organized in the CUII. The prerequisites for a blocking claim against the Internet access provider pursuant to § 8 DDG are met, - if a rights holder can prove his copyright, - his works are published on the Internet without his consent, - he has no other way of remedying the infringement, - if the blocking is reasonable and proportionate.

[0] https://www.bundesnetzagentur.de/DE/Fachthemen/Digitales/Sch...