Interesting discussion, and an unfortunate situation. Thanks to John VDB, as always, for clear explanations of the Rules.
I watched this in real time, and at the moment it happened, and long before I knew anything about the rules official intervening, I didn't see a thing wrong with what Korda did. It's not realistic to expect her to treat that putt just like any other; it was a REALLY difficult eagle putt in the Solheim Cup to win the hole and it just...stopped. I didn't think the time she spent on the ground or the speed at which she got up was excessive at all.
I really like Madelene Sagstrom; I watched her play college golf when LSU came to the big womens tournament at UNC, and she just seemed like a great kid. I don't think there is a reason in the world to think that she hurried to pick Korda's ball up before it fell in; not only does she not strike me as that sort of person, but she would have to be thinking awfully fast to process all of that. She just reacted, and I think any of us in match play might well have done the same thing.
BUT we've all had putts that were partially overhanging the hole, with no realistic chance of going in, and that's what happened here. Whether or not the ball had a chance of going in isn't really relevant; it's only the overhang that matters. Sagstrom just went really fast, and at the moment it happened, that thought actually ran thru my head, if only for a second. I don't think there is anything more to it than that.
As to the official, I don't think sports work very well when officials don't apply the rules consistently and objectively. You hear fans say "Let the players decide the outcome" rather than an official's call on a last second play in football, but NOT calling pass interference that would have been called all game until then DOES decide the game. This official simply applied a rule to that situation; unfortunate but hardly arbitrary.
As to the question of forfeiting the next hole to somehow even things up, that's just silly; there's no way to draw the line on that. Should you forfeit the next hole because your opponent was in a footprint in a bunker? Or when they are in an unfilled divot in the fairway? Or when their ball hits a sprinkler head and goes in a hazard instead of rolling up on the green? That's just not the way sports are played; there is good luck and bad luck, and you just play through it.