When you ground the base, the emmiter-base voltage is -5V. This means the transistor is biased hard on. The junction os saturated. This has the effect of connecting collector to emitter, with like about 0.1V drop. The 5V present at the emitter is present at the collector. With only -0.7V of b-e voltage, the transistor will be Biased class AB and ready for action but not fully saturated, which is where you want to be.
About the PWM, it is a good point, and another reason not to use a 6V rail as the life of the LED will be exponentially reduced as it is overdriven.