Can the Mass Air Flow sensor cause a car to die?

I think the mechanic was just using simpler terms to make the problem, of the direct cause, more easily understood by the lay person.
What the mechanic probably found was that the large black tube the MAF (Mass Air Flow) Sensor is in, was loosely connected at either end. There are some large clamps, usually, which hold the tube in place.

When the air filter was last replaced, the large black tube was disconnected to facilitate changing the air filter. When the tube was put back on, it wasn’t put on properly, resulting in an unmetered air bleed. The MAF Sensor measures (meters) the amount of air entering the engine for combustion. The amount of fuel sent into the engine is metered. The bleed air (air leak) messed up the fuel and air mix, and the engine stalled.
Some less scrupled mechanic may have seen this as an opportunity to sell you an expensive MAF (Mass Air Flow) Sensor.