Because start-up require people to do all kind of stuff. You'll learn front-end and (some) back-end and will have bigger picture, which generally is "A Good Thing".
I currently work at a largish consulting firm and get all those things, plus I don't have to settle for "long hours and low pay". Perhaps "work at a company that lets you work on interesting problems and learn new skills" would be far better advice. There is no reason why that has to be a start-up, nor is there a guarantee that a start-up will give you those things.
True, there's no guarantee. There's no guarantee that you'll find "work at a company that lets you work on interesting problems and learn new skills". Everything here is subjective. :]