In a car, soot (carbon) is produced as a result of VERY incomplete combustion (typically due to too much fuel being delivered for the amount of oxygen drawn into the engine). Soot is the first oxidation state up from that of the fuel itself. Carbon monoxide is also a product of incomplete combustion, but is one step higher oxidation state than that of soot. Complete combustion produces CO2, which has the highest resulting oxidation state resulting from combustion.
The optimum amount of fuel to be delivered into the engine depends on many things, and is nowdays controlled by computer. The computer monitors many things such as coolant temp, manifold air temp, throttle position, engine RPM, manifold vacuum, barometric pressure, oxygen sensor, more and makes a programmed deterimination of the injector pulse width required to deliver the correct amount of fuel at any given moment. This calculation and adjustment is done many times each second. The production of soot indicates the failure of the fuel control system to provide the correct amount of fuel (at some point).
A little soot is normal, as fuel control systems are not perfect. Cars that are driven for longer distances tend have exhaust streams of higher temps and burn more of the soot out of the exhaust.
Excessive soot/black smoke, coupled with poor mileage is a slam-dunk that the fuel delivery/fuel control system is working improperly. This could be due to failure of any of the input sensors or ECU, as well as fuel delivery hardware such as fuel pump/pressure regulator/fuel injectors. Fuel delivery problems with newer cars usually turn out to be related to input sensors.
Sounds to me like the car in question here has a legit problem, unless it is being driven very hard. Full throttle and during initial warm-up of the vehicle are the only times the engne doesn't have closed-loop (O2 sensor feedback) control of the fuel delivery.