During flight school, one of the first things we learn on a piston-single aircraft is to apply right rudder and maintain runway heading on takeoff. Small single-engine planes have a tendency to yaw left due to effects of torque, slipstream, and p-factor. I'm guessing the pilot drifted left on climbout due to lack of right rudder. He could have turned 90 degrees by the time he leveled out at 1500 feet and been over the river. Sometimes as pilots, the worst thing we can do is react. It's usually best to take a breath, think about your situation, cross-check, decide, and act intentionally. By rolling the dice, the pilot had a 50/50 chance of making the wrong decision. I don't like those odds.