This is not true. It's about preventing impulsive suicides, not premeditated ones. If a depressed person is having an episode and all they have in their house is 16 pills, then it removes the opportunity: maybe by the time they've make it to the shops and buy more, the moment will have passed, and a life would be saved.
It's been shown time and time again that you can reduce absolute suicide rates by removing opportunities like this. If I remember correctly, there was something similar involving gas ovens, though I can't find the reference now. Guns, bridges, etc. are all similar too.
When it comes down to it, if someone's determined enough to kill themselves, they will, but the truth is most people aren't and doing things like only selling small quantities of pills really can prevent suicides.