Were the sloppy people at the Delta gate headed South, to FL or GA perhaps? That would explain it, I think. My DH's cousin (in Nicaragua) always thought Americans dressed very casually because the only Americans she ever came in contact with lived in FL. It wasn't until her DD went to college in VA that she realized there are also Americans who dress nicely. She was pleasantly surprised, as the women in Central America don't dress casually.. I know from living down there for 8 years. Even the maids would dress nicely (dress and heels) to ride the bus, change into work clothes to cook and clean house, and then change back into their nice clothes to catch the bus to get back home. They were poor, but clean and nicely dressed. I always thought that was remarkable, considering how they walk long distances just to get to the bus stop.
I personally have taken enough cruises and trips back and forth to Central America to know that just about everyone I've seen in GA and FL airports dress casually. On the other hand, there are some women I know who just moved here from France, and they don't dress any better than I do. I'm not a casual dresser, and I'm not saying they look bad. Not in the least! But it would be a real stretch to say they're more stylish than many American women I know. They aren't.
In the end, though, it's not a good idea to make generalizations unless you're a seasoned traveler, have lived in many places around the world, and are therefore qualified to make them. Who am I to say Americans are all sloppy or that Europeans are better dressed than Americans, or whatever? I haven't been around enough to know. I can, however, comment on how women dress in Central America. I've been there long enough and frequently enough to know. Also, my DH and his family are from that part of the world.