Adding to that - it's not necessarily the GA's final call when to shut the door. It may have just given the OP a false sense of security to say, yes, you can make it, or even to say no, you can't. How is a GA expected to know how fast someone can run? Or if someone will stop & get a sandwich along the way because they were told they still have time. Beyond that, the GA of the connecting flight would be aware of the location of any connecting pax but still can't necessarily hold for them.

I've sat next to plenty of people on flights coming into ATL who are worried they won't make a connection. My advice is always - run! Because you never know if the on-going flight is delayed or if they might be holding because you're just one of many trying to make it. They know where you are. Stopping to ask a GA to call ahead only takes time away from potentially making the flight. For example, I recall on one flight that was late arriving at ATL, the FA made some announcements about tight connections including saying: 'there are 10 people on this flight connecting to CVG, they're holding for you, but hurry!' In other words, we're giving you a chance, but if you lollygag we'll leave you behind.