I found this which does say NSAIDs can cause liver problems, but does dwell on liver related stats for acetomenophen.
Nevertheless, acetaminophen overdose is one the most common causes of OTC drug poisoning in the United States and Britain. More than 30,000 cases per year of acetaminophen overdose are reported to the American Association of Poison Control Centers (Bartlett D 2004). It is a leading cause of liver failure in the Western world and the leading cause of drug-induced liver failure in the United States (Bartlett D 2004).
What is unclear is if acetaminophen is taken much more often than NSAIDs in general, hence resulting in higher statistical instances of liver problems compared to other OTC drugs, but not a fair apples to apples comparison of instances per doses taken.