This quote, or some variation of it, has been bandied about on the internet attached in comment sections to news stories about delayed games for years now. And I think it's well past its truthfulness, at least for the most part. It's not that I think game delays are bad, or that a delay cannot significantly help a game's release, it's just that I don't see how this quote's second half can hold true anymore when we've got obviously rushed games like Fallout 4 in play.
You may disagree that Fallout 4 was rushed, but if they had given that game more time in the oven I don't think we'd have seen nearly half as many problems with content, story or gameplay. That said, games like Fallout no longer rely on their final code to carry their reputations into posterity. The preeminent example, and one that some may think is "cheating", is the revitalized success story of Final Fantasy XIV which launched in a hideous state only to continue its development into one of the most lauded MMOs in recent memory. Yes, it's an MMO and so by its nature it shifts and changes all the time, but such change isn't completely out of the realm for other games.
Post-release patches have rescued plenty of games that could have used more development time. Fallout: New Vegas, to use another example from that series, is worth considering. Its initial state was full of game ending bugs and weird glitched out NPCs and items. Now, not only is it playable, but it's looked back on as easily better in many regards than Fallout 3 OR 4. Nintendo's design philosophy is likely in the middle of a big change, with a new president, a new console, and a new mobile market all in play. Looking at Smash 4 is proof enough that Nintendo has taken well to the idea of post-release support. They regularly update the game with unannounced gameplay balancing patches (which invalidate your old replays, rawr!), and is something I very much did not expect them to do this far out after release.
Bear in mind, I'm not saying that this bold new future is amazing. Plenty of companies, like Bethesda, are probably using this fact to their advantage and to the early consumer's detriment. When a game's worst possible state is when it's being the most heavily advertised, you've got a system that's being less than honest. It all stops short of false advertising (usually), but a game's release is probably not the best time to jump on board, even though early adoption is exactly what is requested.
To reiterate, I only find the second half of that quote no longer totally true. Delayed games definitely have benefits to the game's overall quality, and like many people these day I find myself happy at the announcement of delays since it means the game will be better for it. But with the nature of things like early access "releases", a game's actual release date is almost made arbitrary compared to the total finality that it once represented not too long ago. Minecraft's release date didn't really signify any tremendous change for that game which has been publicly playable for years before. Many of Steam's worthwhile early access examples have also released under similar circumstances, like Nuclear Throne. The quote's not all together useless, it's just outdated.