That's correct. It can start with one institution and then spread throughout the financial system, such as was the case with Lehman Brothers and the major insolvencies of the U.S. investment banks.
It can also start in these major clearing systems. The clearing systems really act as funnels where unbelievable amounts of money are funneled and cleared through the system in money and assets every day. If those systems are not sufficiently protected from risk and they fail, that's another form of systemic risk that will cascade through the system.