I once experienced a situation like that, when I was seriously presenting the results of a study, someone interrupted my conversation and everything went bad. Because the information I have prepared suddenly changes and disappears, there is a risk that errors will occur.
Since then I have learned to appreciate the speaker in front of me by listening more to what is being said and waiting for the right time to rebut or ask questions. Maybe this is the right way to get good results.
Maybe the tips you give can be very useful for me to apply to all my activities. Coincidentally, I also work in a public service and all your tips will be very useful for me to apply to the people I talk to at work. Thank you brother @galenkp, if we want other people to listen to what we talk about, then we also have to listen to what other people talk about.
That's one of the risks of a person interjecting, it can shift the entire focus of the conversation or people in the room and unless managed quickly and well can derail the communication process pretty quickly. You learned from it though, from someone else's mistakes, and I'm sure you've put those lessons to good use. Maybe, this post will give you a few tips you can take a way and use also.