It's not the same thing three times though, and the context of this very discussion should tell you that.
Each of the three components is radically different, but there shouldn't be much redundancy - each of the three serves an entirely different purpose and only one actually contains the core information you need to remember.
The introduction ("you tell them what you are going to tell them") is warning you what's coming. That means giving you context and a road map for the information that follows. Think of it as, say, the marketing blurb for the book you're about to read.
The second ("You tell them") is the information. This is long, and your brain under normal circumstances isn't going to be prepared for that information. Hence the warning and roadmap.
The last ("then tell them what you told them") is the reminder, the overview that makes it easier to remember the information. It's the roadmap for returning here, rather than the simplified roadmap for finding your way there for the first time.
If someone is repeating the same thing three times, they're doing it wrong. As you saw, it's easy to set context without being overly redundant, and a reminder of what you just heard is always helpful.
Out of interest, while this was a little TL;DR (doesn't matter if you're stuck in a meeting ;-), did you feel it was overly redundant? The "Each of" paragraph was "you tell them what you are going to tell them", the "If someone is repeating the same thing three times" was the "then tell them what you told them". The bit in the middle was the core information. I'm not a great communicator, but I doubt you spent the entire thing saying "Why does he keep saying the same thing over and over again? What a jerk!" But if I'd launched into just that middle part, and not provided context, it wouldn't have immediately clicked as to what relevance it has to your concerns.