People overdose because heroin is illegal, not because they are users of the drug. As I pointed out above, consistently using a consistent amount of the drug presents at most a minimal risk of overdose, but because of the war on drugs, users have no way of being assured that what they get has uniform consistency (or, for that matter, that it is in fact heroin; as the link I posted above indicates, it's quite possible that what killed Hoffman was actually fentanyl). Regulating the drug would solve that, but it's impossible to regulate a black market, because it's a black market. Drug addiction is a health issue, and treating it as a criminal matter kills drug users.
And as far as I'm aware Brand has been sober for quite some time, but whether he is an addict or not is irrelevant to his point, which is that the war on drugs causes overdoses.