I've seen that quote floating around and never much liked it. For those afflicted with long-term treatment resistant depression, it's more like "a guaranteed solution to a permanent problem".
A lot of anti-suicide advice can seem like a sick joke, little more than empty virtue signaling. Want to really help? Offer a friendly ear and a sense that you really care about the person in question, and stand behind that over a period of time.
Being depressed is generally not a temporary problem. Many of us have suffered it for decades. It may wax and wane, but it's often not something that just goes away. In my opinion, it's something that many of us simply have to learn to live with, as with so many other chronic diseases.
Because everybody is different and even if you have been through it yourself, your experience may be nothing like someone else's, and just because it was true for you, doesn't mean it is true for them. Yes, some people get past it, either on their own, with therapy or with medication. Some people are just numbed by it, other people learn to cope even if it never actually gets better. Other people still struggle every day. You cannot know what is going on in someone else's head or the struggles they face.
Its true that many people get better, certainly with treatment, but a large number of people do not (someone else here said that treatment does not work for approx. 1/3 of people).