No. The entire weight of the water has to be supported by the riverbed because of Earth's gravitational pull on all of the water, not just the part at the bottom. If the riverbed was only supporting the water directly above it (whatever that means...) the rest of the water would just fly off into space. Draw a free body diagram of the riverbed. Or for an easier place to start, grab a cup of water and put it on a scale. Fill it a little bit with water. Fill it a little bit more. Fill it a little bit more. And watch the scale continue to rise. Water is not weightless, whether at the top, middle, or bottom of a cup, pool, or river.