Lying press?

Given that there unquestionably are neo-Nazis protesting in Germany, it pays to tread carefully here.

Wikipedia has an entry for 'Lying press'. It gives us a potted history of the term in Germany:

Lying press (German: Lügenpresse, lit. 'press of lies') is a pejorative political term used largely by German political movements for the printed press and the mass media at large, when it is believed not to have the quest for truth at the heart of its coverage. It can be considered synonymous with the term 'fake news'

History

The term Lügenpresse has been used intermittently since the 19th century in political polemics in Germany, by a wide range of groups and movements in a variety of debates and conflicts. Isolated uses can be traced back as far as the Vormärz period. The term gained traction in the March 1848 Revolution when Catholic circles employed it to attack the rising, hostile liberal press. In the Franco-German War (1870–71) and particularly World War I (1914–18) German intellectuals and journalists used the term to denounce what they believed was enemy war propaganda The Evangelischer Pressedienst made its mission the fight against the "lying press" which it considered to be the "strongest weapon of the enemy".After the war, German-speaking Marxists such as Karl Radek and Alexander Parvus vilified "the bourgeois lying press" as part of their class struggle rhetoric. The Nazis adopted the term for their propaganda against the Jewish, communist, and later the foreign press. During the protests of 1968, left-wing students disparaged the liberal-conservative Axel Springer publishing house, notably its flagship daily Bild, as a "lying press".

Interestingly, in the news bulletin on tonight's PM, the BBC's Jenny Hill mentioned that far-right demonstrators in the German city of Chemnitz have been shouting that very term at media today, but she shrank its history down to just the Nazis:

NEWSREADER: Thousands of people have gathered in the German city of Chemnitz for rival protests over the killing of a German citizen which has been blamed on immigrants.  Police officers from all over the country have been deployed to keep the peace after violent demonstrations by far-right groups in recent days. Our Berlin correspondent Jenny Hill is there. 

JENNY HILL: German flags flutter in the wind as thousands of men and women, dressed in black, some carrying white roses, fill a large section of what is usually a busy ring road. Mounted police officers look on as the protesters chant the old Nazi slogan 'Lügenpresse', or 'lying press' at TV crews. The demonstration has been organised by several far-right groups including the anti-migrant party AfD in protest at the death of a German man, apparently at the hands of immigrants last weekend. Counter-demonstrations are ongoing too. The authorities expect at least 10,000 people to take to the streets of this troubled city. 

She's far from alone is doing this, of course. Many media outlets from across the world (from Time to Haaretz, from The Economist to The Washington Post and The FT) have been saying that its revival is a sinister echo of one of Hitler's favourite terms of abuse. Here, for example, is The FT: "Mr Trump’s attacks on the “lying media” for pointing this out have strong echoes of Adolf Hitler’s demonisation of the “lugenpresse” — the lying press."

Are they - and Jenny Hill - right? Or are they lying, and smearing?