If you do six hours of exercise burning 1000 calories per hour, it's physically impossible to compensate that away: in that day you burned at least 6000 calories, and more realistically upwards of 7000 (keeping your body alive for another 18 hours, building/repairing muscles, etc). I guess the article conveniently leaves that out because it's largely irrelevant: few people are able to invest that amount of time into their diet.
That being said, I would always tell other people that to key to weight loss and maintenance isn't "dieting" it's finding a combination of cutting back on how much you eat and exercise that is sustainable for you long term.
The other part of the equation is that realistically, unless you are already in shape, your body can't handle the intensity required to burn 1500 calories in a day in a reasonable amount of time. If the most you can handle is walking 4 miles an hour, you'll be walking three or four hours a day. I know people who run 6 miles a day in the morning and in the evening but it took awhile to build up to that.