A person who's got strong muscles and doesn't get winded and is light and fast on their feet is going to have a real advantage in a fight -
Depends on the nature of the 'fight.' For the most part, self defense in real world encounters is more about mental preparedness than physical preparedness. You need to be able to act without freezing and to make quick decisions under pressure, which are actually unrelated to physical fitness. If you're trying to run from an attacker, this become more of an issue.
The fact is that obese people are like people who are at a healthy weight; some are weaklings and some are incredibly strong, while most are on par with everyone else. So having strong muscles really isn't the issue; the 400 pound instructor might have had very strong muscles. The fact that you couldn't see them doesn't mean that they aren't there. Refering back to Big Van Vader, look at how he moves in the ring (yes, I know pro wrestling is scripted); he's as fast on his feet and as graceful as any of the more ripped and cut guys, and there's no arguing that he's incredibly strong and has good technique for the sport of his choice.
And scripted or no, in their prime, I would put my money on Vader (his real name is Leon White) against most martial arts icons, including Jackie Chan, Donny Yen, Jet Li, Bruce Lee and Chuck Norris.
especially in a sport-style art like the poster was talking about. It's certainly possible for an obese person to be skilled at techniques that can harm someone, but they're going to have a disadvantage over someone in better shape.
Sure, but since we're talking sport here, the person he was talking about was an instructor. Look at boxing coaches. Do you think that Cus D'Amato could have whooped Mike Tyson? Cus made Tyson a champion by helping him to be at his best in the ring, not by being able to win matches himself.
Also, just... someone that's exercising even a few hours a week and eating a reasonably healthy diet will not stay obese. They might not look like Bruce Lee, but they won't be 400 lbs. And in a sport-style art, they should be getting in at least a few hours a week of decent exercise. So why are they still obese?
Depression and stress can wreck you physically. Both are linked to many physical ailments, including obesity. Depressed people sometimes don't make healthy lifestyle choices. Depression is a medical condition, and while it doesn't affect your physical condition directly, it can affect it indirectly, and can do so quite thoroughly.
Then you have eating disorders, which are also medical conditions, which may be induced by other factors, including depression and stress.
Keep in mind the context of this discussion; none of us are stumping for sumo wrestler looks. The response has been to conflating an instructor's personal health issues with McDojo-ism and with an instructor's personal health issues being reason to mistrust their ability to teach.