Yes, that advice makes a lot of sense. Too much focus on grammar indeed can hamper learning how to speak in English—and I’d say in learning how to speak any language for that matter. It just makes the learner too self-conscious and too fearful of making mistakes to the point of being tongue-tied and inarticulate. Let’s keep in mind that even in the absence of formal grammar lessons, the child learns to speak and become adequately fluent in a particular language simply by listening to members of the household communicate with it. The child learns to speak a language primarily by imitating its speakers, and the more fluent the people around the child are in that language, the faster the learning process and the better will be the child’s command of it. This obviously applies to English as it does to all languages.
When it comes to writing, however, the situation becomes different: the learner should first learn enough of the vocabulary, grammar, semantics, and structure of the language to be able to put his ideas in clear, understandable writing. As we know, this is a much longer and more painstaking process than learning to speak the language, so it’s no wonder that we sometimes meet professionals who speak English very fluently but whose English grammar is so atrociously faulty that they couldn’t even write a decent sentence longer than five or six words. It is for this reason that every nonnative English speaker, whether young or adult, needs to undertake a continuing self-improvement program in English grammar and usage to be able to speak and write it fluently. Not to do so is to risk making do with faulty spoken and written English for life.