German laws (being structures after the civil code) are intent based, which differs from the british common law derivatives which work by the letter.

Hence the important question resulting from that quote is: Does the driver derive taxable income from the activity of driving the car?

Getting $20 for the one-off trip won't get you there, not by a long shot.

Getting $20 for every time you're driving people to the airport 20 times a day, 200 days a year is a different matter (assuming a short trip where $20 work out).