Red LED light up at 1.7V with resistor?
Your model of the LED is too simple for this situation. Here is the first LED I found a datasheet for: 



As you can see, the voltage varies with the current. Different LED construction and materials will result in a bit different curve (and it will vary slightly from unit-to-unit even for components of the same model), but the important thing qualitatively is the shape of the curve, it takes less voltage across the LED to push a very small amount of current through it, and your eye is quite sensitive to low light levels so a tiny amount of current may be enough to produce visible light with a good LED.