Besides presenting the wrong graph of relations in the language remarked upon already, the statement gives the sense to someone uninformed that modern German is a pretty old language.
So again, why does this apparent misunderstanding matter? It certainly doesn’t detract from the article that a less precise colloquialism was used.
Both share a common ancestor. A lot further back than the 16th century. At the time that the branch that became English came into existence, German didn't exist either. It was just Frankish, or Alemannic.
At the time the Angles Saxons and Jutes left the continent, what eventually became German looked like this:
https://en.wikipedia.org/wiki/Bergakker_inscription
And it was already a separate language from the Angles' language