For a long time I've been an opponent to this mantra and in a way I still am. This is because in my opinion a lot of people define "higher quantity" wrongly. Learning flash cards mindlessly all day will hardly help you become more fluent in a foreign language; preparing loads of meals or even the same meal very often doesn't help you become a chef if you aren't fully concentrated on what you're doing.
Lately I am of the opinion that you have to practice with a zen attitude, like it is described in "Zen Mind, Beginner's Mind". And because of that I think the author of this article also gets it wrong when he says:
As Ira Glass so famously put it, the best way to refine your craft is to create a huge volume of work. Not to create the most perfect piece you can, but to create many pieces of work.
I guess what Mr. Glass hints at is that you shouldn't become paralyzed by being caught up in thoughts. That is: It is useless to think "Oh this needs to be perfect" or "Oh this needn't be perfect because some clever guy said so" because in that instance you've already lost concentration and you are not really stretching your skills. You certainly have to TRY your best every time. In other words: Strive for perfection but don't get distracted by having dualistic thoughts about your practice.