I've always interpreted this message as "don't assume that everyone you're interacting with has all of the same context as you" and be proactive about sharing relevant context whenever you communicate. Not "send people the same message over and over or annoy people to make it seem like you're staying busy"
Maybe we're getting hung up on the definition of what 'over-communication' means. I don't disagree with you that there's a failure mode here, but as a mindset it's helpful when approaching your interactions with various functions in the business to keep in mind that communicating things that seem 'obvious' to you (because you think about them and talk about them a lot) might be really valuable to share with whoever you're talking to.
An example: I'm meeting with a sales rep who has a customer pushing really hard for a specific feature. It might be a good opportunity to walk them through what the overall strategy is over the next six months to help frame where their feedback might fit into it (or to explain why it doesn't and why we're unlikely to work on it). I might have shared this a month before at an all hands, but I can emphatically say from many past experiences that repeating it is helpful in these scenarios, even though it feels like I'm 'over communicating'
The other things listed out in the article feel like tactics that can help here, but for me 'don't assume everyone has the same information you have' is a really helpful mindset to hold.