You can kill yourself with almost anything, including water.
Did you read the article? The whole point of it is that the dose of acetaminophen found in many pills in the US is dangerously close to the level at which liver damage occurs.
The same can't be said for other painkllers.
(Edit: Googling for "aspirin suicide", find it in top 20 list of suicide methods http://wantdeath.blogspot.de/2011/07/method-5-of-suicide-asp... )