Weight is won or lost in the kitchen. Full stop.
A 1 hour run might burn 500 calories. If you go and eat till you are not hungry, you can easily eat 800 or 900 calories. You are not going to lose much weight at the method.
There is still a lot that we don't know with regards to metabolism. I am usually a higher mileage runner during spring to fall months (70-90km / week) and although I scale my eating to offset my calories burned, I will still lose weight. I will not provide a citation but it's quite widely known that metabolism increases as the body normalizes into a training period or regimen. And increasing with diminutive returns as the training increases. Recovery also burns more calories even while sedentary (as you should be when recovering).
Of course the body can/will waste calories, burn them at a higher rate depending on other things. That's not most peoples' problem though: unexpectedly losing too much weight. There's not a billion-dollar industry around that issue.
I think this is disingenuous. Certainly regulating caloric intake has more impact than exercise because it's "easier" to achieve a caloric deficit, but that doesn't mean running isn't great for weight loss all else being equal.
Furthermore, exercise is important for other health reasons. So maintaining the same caloric intake and adding running is much better than simply reducing your caloric intake by the same amount.
Of course it's possible to eat 1000 calories' worth of food in one sitting, especially if you're eating something with tons of carbs in. But if you keep your diet roughly the same and go on a 1 hour run three times a week, you'll definitely start losing weight..
(The idea that sport can't help you lose weight is still ridiculous of course, even if you are only burning 600 calories per hour. Bad habits make you overweight and establishing good habits (like exercise) is the key to get out of that.)
It'd be nice to have an outlandish comparison to put towards their claim.
The 300 kcal of work equate to ~349 Watt hours as WolframAlpha will tell you, so if you want to produce that in a single hour you need to continuously put out 349 Watts.
Now we have put lots of humans on scientific ergos which can accurately measure work, and that is a very high number for a single hour for any individual. There is a chart here that gives you the kind of work rates achievable by category:
http://d4nuk0dd6nrma.cloudfront.net/wp-content/uploads/2009/...
It's normalized by weight but it's more accurately height, someone weighing 300lbs isn't suddenly going to produce more power than at a normal weight. The number you're looking for is "FT" or Functional Threshold, which is generally assumed to be around the absolute maximum average power sustainable for an hour. At the end of that you should fall over and puke your guts out. So for someone doing 350 Watts for a hour, that would put them at world class or domestic pro level.
[1] http://well.blogs.nytimes.com/2015/08/07/walking-vs-elliptic...