It is in your original statement (abbreviated):
If there were easily exploited buffer overflow in <our program>, ambulances and fire engines <for our customers> would never be called to their destinations nor arrive on time.
One doesn't follow from the other. Your statement implies there are bad actors in existence that would actually exploit such flaws in order to disrupt the service. That may or may not be true, therefore it does not follow.
> The previous poster purported that I mustn't have much "real world" experience in coding, and I responded that I and my team wouldn't be entrusted to successfully maintain a program and network that coordinates emergency services first responders over a large land mass and number of people if that was the case.
That's not what I actually replied to, but it's also a non-sequitur. It would be entirely plausible that you could be a reckless band of cowboy coders that happens to be able to produce a working product that is nevertheless full of theoretically exploitable flaws that just happen to not get exploited, because nobody cares. Also, whoever "entrusted" you may themselves be entirely reckless or incompetent.
I'm not saying that any of this is the case, I'm simply saying you can't logically deduce one from the other. Therefore it doesn't really work as an argument.