From what I know of any criminal investigations the prosecution has no input into investigating or evidence gathering, deciding only if it is sufficient to lay charges to present for prosecution.
I rather think some people who are caught up in personality rather than substance and misconceptions about what Herr Walters actual role is. It was never only his show - it was always a joint effort with BKA in the lead.
I think 'spokesperson' is the word they might be looking for but very obviously haven't found yet.
In Germany it varies. The police have an obligation to investigate every single crime reported. The prosecutor's office has the duty to investigate and pursue any matter in its jurisdiction as soon as it learns that a criminal offence may have been committed.
Prosecutors are authorized to undertake investigations themselves or can request the police to do so and the police are obliged to carry out such requests. Moreover, prosecutors can order witnesses and expert witnesses to testify before them.
A prosecutor is usually only involved from the very beginning in homicide or serious white-collar crime cases. Police also contact prosecutors at an early stage when significant publicity is expected or they need help gaining a judicial arrest or search warrant etc., or when the Ermittlungsrichter is to interrogate a witness.
https://en.wikipedia.org/wiki/Public_prosecutor%27s_office_(Germany)
