Contrary to conventional "wisdom", high power LEDs behave far more like a resistor than a diode.
Is that what we are talking about here? I associate 'high power' LEDs with those that are becoming available to replace household incandescent bulbs etc. The LEDs being used in flat screen TVs could well fit into this category as well.
I would think that any LED backlight that is being driven by an output pin of the Arduino would be classified as low power, and it would behave much like any diode, not like a resistor.
Don