The big picture is that the FAA doesn't want the public to confuse the safety record of an airline with somebody flying a puddle-jumper (daily crashes in USA). The flying public just expects to get there without doing a risk evaluation, and puddle-jumpers are far riskier than airlines.
When you rideshare with Uber, there is a question of insurance.
When you rideshare a single-engine piston plane, there is a question of your life.