I think 'don't drink' has to be backed up by other support measures. I can make the choice to 'not drink' while I reach out for support. When people say that, I think they are asuming it's meant to be part of wider overall recovery strategy, not the only strategy. I think if I ONLY had 'don't drink' as a recovery strategy, I wouldn't make it. I think it has to be taken in the context of a wider recovery message.
I go to therapy, I'm taking medication to treat alcoholism (naltrexone and campral), I have a sponsor and I go to meetings. In that context 'don't drink even if your ass falls off' is good advice. If I was just sitting at home struggling with the obsession and compulsion with no other support system, I would kill myself because I couldn't deal with what happens inside my head and the desperation of the need to drink.
The mental, emotional and physical discomfort of withdrawing from alcohol abuse is almost intolerable. Most people need more than 'don't drink'. That's just the first step (not in the AA sense) towards getting the help I think all alcoholics need to stay stopped.
Maybe 'don't drink and get professional help' is a good strategy.