Soap does, lather the dog well and let the soap sit there for a minute, the soap breaks the surface tension of water and the fleas drown. You can see this work if you put a few drops of soap in a cup of water and drop a flea in. Without the soap the flea will jump back out using surface tension of the water, with soap the flea will instantly sink and die. This is also why fleas die when you wash the dog blankets with laundry soap.
