Well. Like any other generalisation, this statement simplifies things of course. However, getting a good understanding of grammar might be more important in the process of learning German than in many other languages, and paradoxically perhaps, more important than learning vocabulary. Of course you can't say anything without knowing the words to express your ideas, but once you know a fair share of words you hit the brick wall of German grammar soon after.
One of the most important lessons that students need to learn is thus how to send their ideas through a grammar filter to check what they can actually say in German when translating from their mother tongue and where they need to place words in their German sentence. Ultimately, German is a language in which most sentences work like a composition. A composition, you might wonder. Why a composition? Here's one example:
Having checked whether they wish to go for standard word order or emphasise any other element in their sentence (such as the time), most of my students think very carefully about the grammatical consequences of the verbs they intend to use and whether they'll have a second verb at the end, before they figure out the middle bit between subject, the conjugated verb in second position and their main verb at the end. Screening their sentence for an indirect and direct object, for a genitive, the correct tense, prepositions, adjective endings and so on, my students understand that they master the language when they understand its grammar.
Here comes the caveat: German words, especially its verbs, are, for the most part at least, very precise and context-specific. Anyone who ever tried to translate the English word "put" into German will understand what I mean. For anyone who doesn't: there are more than five different translations of the word, depending on its exact position. So, to argue as I did above that German is 75% words and 25% grammar, might seem false, as there are so many different words to learn. However, having learned the words, it's still the grammar that determines everything after that.
Is it a challenge? Yes! Yet, is it also rewarding? Very much so. Find out for yourself!