To me the essence of that phrase is "No one (worth spending the time to associate yourself with) cares if you stutter (if disclosed). Your coworkers probably won't care that you stutter. But right now they have no idea that you stutter, ans just assumed that was just an everyday hiccup that probably happens every once in a while to new employees. Treat it like just another one of those "good rule of thumb" type phrases. Like "good things come to those who wait", "early bird gets the worm", etc. Obviously there is going to be a lot more to these situations than a half sentence long phrase, but they will generally be a good nudge in the right direction. It is unreasonable to expect them to hold true all of the time. Personally, having that idea in the back of my head even just subconsciously helps me in social situations tremendously.