I'm a native Dutch speaker. From my experience is that Dutch speakers can understand German in very broad strokes without ever having had a lesson. Germans not so much. I always thought it was weird that it works in only one direction, but I think it does come down to the wildy different pronounciations in both languages.
Certain German words almost sound like the Dutch word, only it sounds like the Dutch word has been put through a "Gobblediegook" filter in the German version of the same word. But it does allow Dutch speakers to sort of guess what the word would be. Of course, this isn't always the case, sometimes you get German words that sound a lot like a Dutch word but have, in fact, completely different (and sometimes opposite) meanings.
In Belgium this has lead to a funny occurence called "Koeterduits" ("Stupid German", German as in language, not a person). This happens when a Dutch person, who has no workable knowledge of German, tries to speak German by just "Germanifying" Dutch words by changing the pronounciation, adding some extra syllables and speaking in a German accent. This never really works, as the German recipient in the conversation will be unable to understand what the Dutch speaker is saying, while the other Dutch people bend over laughing. My ex-husband has to speak German in his dayjob and I would sometimes start to speak "Koeterduits" to tease him, since it can be really confusing to listen to.
I remember my very first lesson in German in high school. Our teacher was speaking only German, but we could all understand him. Although I do suspect he was keeping his vocabulary somewhat limited to words that were close to the Dutch words. Years later, after my working knowledge of German had faded into obscurity, I was on a weekend Holiday where a friend apparently was speaking German (they were doing a comedy sketch) and only four or five sentences in did I realize he was speaking actual German instead of Dutch with a German accent.
I do find it really funny that German always seems to have way too many syllables in words. Take, for example, "nurse" is "Krankenschwester". I just love that, such a mouthful.