There's nothing wrong with having good personal discipline, but the notion that you can scrimp your way to wealth by eschewing $5 daily coffees is absurd.
Not to mention, that's $5 daily coffees and...nothing else, as there's usually not a second thing you can cut back on in these preposterous examples, and once you've cut back the coffee once, that's it.
One final thought: often the people who say this have zero experience with actually living close to the poverty line. A cheap, unhealthy, delicious indulgence on the daily can make living with less feel much more palatable - or at least, suck less hard. It's not "disciplined" but it'd be a hell of a lot easier for me to be disciplined with my fancy life full of excess.