That's true, but people tend to misunderstand this.
Of course sprinting all-out for 5 minutes is better than walking for 5 minutes. If all you have is 5 minutes, and you're trying to get the most out of that session without any other consideration, you should sprint.
But for most people, 5 minutes of all-out sprinting is very, very hard, and has a very fatiguing effect - you won't want to (or be able to) exercise again for a while. As opposed to walking, which most people can realistically do for a long time.
The concept here is the amount of fatigue you're accumulating. As a fat-loss tool, a low-fatigue exercise that you can do for a long time will mean much more total calories burned, as opposed to a high-fatigue exercise you'll only realistically do for a very short duration.
This reminds me: Scott Adams said the optimal exercise routine is the one that maximizes your chances of exercising again the next day. A good way of thinking about it.
What about a ladder workout? We did these in track and field and it was a brutal burn that would send people puking by the fence by the end and not being able to walk up stairs for a few days after. You'd run a 100m, short rest, 200m, rest, 300m, rest, 400m, rest, 300m, rest, 200m, rest, 100m, then you are simply cooked. Two weeks of this though and you are whipped back into shape for track season.
I don't have exact figures, but the amount of calories burned in very strenuous activity is about 3 times "light" activity like walking (I think - would love a legit reference though!)
So let's say you do the ladder routine. I don't have any idea how fast people typically sprint, but let's take 2 minutes per sprint - we have 100 twice, 200 twice, 300 twice, and 400, for a total of 7 sprints - so we'll say 14 minutes (and I think I'm exaggerating up?) In terms of calories burned, this is the "same" as a 45 minute walk.
I assume, by the way you describe it (people can't walk up stairs for a few days, people puking) that this is very hard on people. They're probably not doing this every day.
As opposed to walking 45 minutes, which is incredibly easy and won't make anyone feel bad, and you can definitely do every day.
Of course, I'm only talking calories burned here - for health and for improving conditioning, of course you need something more strenuous!
Of course sprinting all-out for 5 minutes is better than walking for 5 minutes. If all you have is 5 minutes, and you're trying to get the most out of that session without any other consideration, you should sprint.
But for most people, 5 minutes of all-out sprinting is very, very hard, and has a very fatiguing effect - you won't want to (or be able to) exercise again for a while. As opposed to walking, which most people can realistically do for a long time.
The concept here is the amount of fatigue you're accumulating. As a fat-loss tool, a low-fatigue exercise that you can do for a long time will mean much more total calories burned, as opposed to a high-fatigue exercise you'll only realistically do for a very short duration.