Based on the nature of causal claims: A lawsuit or someone claiming liver damage due to taking said medicine, in order to prevent any future lawsuits the company or producers of acetaminophen have to claim this could be a potential side effect, even if the person who sued had nothing to do with acetaminophen.
Jack's reaction was exaggerated and unreasonable, even in the case that acetaminophen COULD cause Liver damage, a person would have to be taking it at least every day, every four hours for at least a couple of years. Based on this, painkillers are usually taken in instances of accidents, random or chronic pain, unlikely to be used so often. The random use of painkillers will most likely NOT cause liver damage and taking acetaminophen does not automatically mean every acetaminophen user will have liver failure.