I believe this is very dangerous advice from your friend, and I would bet that he joined MBB in a rather junior role (Business Analyst or (Junior) Associate).
Generally, speed should be the LAST THING you worry about when building your case solving muscle! Similar to learning an instrument, you HAVE TO do it in a slow and meticulous way in order to properly learn the "craft and art" of case solving. Increasing the speed of framing, structuring and solving the problem is just a natural consequence of you increaslingly mastering the whole process.
Taking MORE time in the beginning typically saves a lot of time over the duration of the case when you know how to rigorously define the decision logic which will allow you to anser the precise question of the client.
From my experience, trying to just focus on speed is practically ALWAYS damaging! It is also damaging to try and become lightning fast with math, because this invariably damages the quality of your communication and your ability to take along the interviewer to follow the stringence of your analytical thinking (the interviewer will always assume that the way you behave in the interview is also how you behave with the client, and if you are hard to follow because you are doing multiple steps of math in your head at a fast pace, then this is damaging to you because you are harder to follow for a client!).
So my advice is: get your case skillset right! Learn how to set up a bullet-proof top-down logic how to answer the precise case queston. Then, speed is a natural consequence, since you will be able to cut through all irrelevant noise and immediately discuss the core of the issue. Trying to increase speed in an isolated manner usually creates more harm then benefit!