Push describes it correctly.
I personally wouldn't go directly onto the yeast from the previous batch without adjusting for pitching rate and getting rid of the dead yeast. Overpitching and dead yeast will both contribute to off flavors and less head retention in the finished beer.
The quick rinse lets the dead yeast, hop bits, and other crud drop to the bottom of the container.
Use the pitching rate calculator at
http://www.mrmalty.com to figure out how much of the yeast cake to use in the next batch.
Two simple things, but they help make for consistent and proper fermentations.