Eight years ago this month, Lehman Brothers failed in large part due to panicked hedge funds pulling their money. With some big hedge funds worried enough to cut their exposure to Deutsche Bank AG, the parallel is obvious—but also deeply misleading.

Deutsche Bank’s shares have plummeted in recent weeks after The Wall Street Journal reported that the U.S. Justice Department suggested the bank pay $14 billion to settle allegations around mortgage securities. The bank expects to agree to a lower figure.

Some...