That statement is incredibly misleading.
Criminologists aren't anywhere close to a consensus on the causes of the crime rate reduction of the last few decades. Many theories have been offered, from decreased crack use, to fewer unwanted children resulting from legalized abortions, to your suggestion of harsher sentencing.
Yes, Harsher sentencing may have something to do with it, but it could just as well have increased our crime rate and been counteracted by one of the other factors.
There is no scientific consensus to support your claim.
Whether or not the decline in violent crime justifies the rise in imprisonment and the decline in prison standards, or whether there might be other ways to achieve the same declines are different questions. But the United States has become significantly safer over the last ten, twenty and fifty years.