I see credible claims that Switzerland has reduced overdose deaths from opiates with this strategy, but none saying they've "effectively eliminated" them. I didn't look very hard, and you see familiar with the subject. Can you point me to a resource establishing this?
The thing I see reports saying Switzerland has effectively eliminated is deaths due to needle contamination. That's not hard to believe (but then, you could get that effect by giving addicts clean needles).
In the article you posted, I see Hari saying that Switzerland's practices have eliminated wounds and abscesses he attributes to drug contamination. That, too, is very plausible. But most opiate fatalities are not caused by injection site wounds; they're caused by overdose.
I think there might be some confusion. Switzerland itself claims that nobody has died from overdose of officially prescribed heroin. That, too, is totally plausible. But Switzerland still has a street opiate drug market problem!