Note Greenspan's sleight-of-hand here:
When the current crisis emerged, it was assumed that the weak links would be unregulated hedge and private funds. The losses, however, have been predominately in the most heavily regulated institutions – banks.
Passing the banks off as "heavily regulated" ignores a pair of inconvenient truths: 1) the Fed on Greenspan's watch declined to regulate the out-of-control mortgage lending practices of both banks and non-bank lenders, despite having the authority to do so, and 2) investment banks were not subject to the same capital requirements as commercial banks .
Whether or not they were "heavily regulated" during the Greenspan era, banks were not effectively regulated. And non-bank mortgage lenders were effectively not regulated at all.