Really? Almost all other MMI books/vids talk about the 1-2 sentence recap of the prompt before you dive into your answer
The interviewer knows the prompt very well as they've prepared beforehand. You should know the prompt reasonably well as you carefully read it prior to entering the room.
What purpose does restating the prompt (which the two of you know already) verbatim as per what is written on the door before you entered, serve?
It's not necessary. If you like to do so because it gives you more time to think as you verbalize the scenario and doing so makes you feel more comfortable, then that isn't an issue as long as you don't spend too much time on it. Alternatively if you use it quite briefly to help frame your response and you feel it helps your personal sense of flow of your answer, that is fine. If you do so because you're genuinely unsure about some aspect of it, that is what it should be used for.
But to restate the prompt at each MMI station to start off all of your answers as a matter of routine because you read it recommended in some MMI prep resource doesn't make much sense if you feel it doesn't benefit you in your subjective sense of your ability to answer the question coherently.
Personally, I think it is poor form as it objectively does not add anything to your response or in any way give you any marks on the interviewer's assessment sheet. You're really just doing it for your own comfort--which isn't a bad thing, as long as the rest of what you say is meaningful in the few minutes you have with your interviewer.
In my opinion, you're better off answering the question directly after introducing yourself. Also consider that the interviewer has likely heard many other applicants unnecessarily repeat the prompt verbatim to start off their answers and how boring and contrived that seems when it serves no purpose and you are the 10th person to do that on that day. If I was the interviewer, I'm just sitting there nodding my head, trying to stay awake and feign interest until you get to the part of your answer that I actually want to hear.
Ultimately, do whatever you feel most comfortable with and that which feels most natural to you.