when the input voltage is the same as the forward voltage of the LED
But that's the wrong assumption.
If you look at the page you linked to, the pwm waveform has a voltage output of either 5v or 0v, at any given point. If you were to held a steady 5v to your 3.3v led, it would have burned out quickly.
What pwm is doing to leds is to turn on the leds, abusively at 5v, quickly. Because of pov, the led looks dimmer when the duty cycle goes down.
The nice thing about diodes is that they are very good at taking high peak current for a short period of time - sometimes 100x or 200x of their rated current.