I happened on this by accident, and there is nothing like adding comments to an old fire.. But...

If you are driving the LED from a source with very low internal resistance than the LED will be sensitive to small changes in supply voltage. If you are driving the LED from a large power supply capable of delivering amps, and it drifts 10MV higher, you may cook the LED. Note that in many instances, such as inexpensive flashlights, the LED's are seen as disposable and they are pretty sure the battery terminal voltage is not going to be more than whatever is normal for that type of batteries chemistry; The LED probably operates over spec or right on the edge with fresh batteries. Also, depending on the devices forward conduction curve, you may not be able to get say 20MA into a white or blue LED on a 3.3V supply. And if you do the math, putting a 5 ohm resistor in series with the LED is not going to buy you a lot of voltage latitude. However up to this point we have only been concerned with the health of the LED, which seems kind of simple minded. I would be much more concerned about over stressing one of the I/O pins on a microcontroller that cost me a few bucks than cooking an LED that can be had for under 2 cents on eBay. So, if I were to connect an LED to the output of an expensive chip with a 3.3V Vcc, even if the LED was rated at 3.3V I would probably add a few hundred ohms and run the LED off just a few ma than risk damaging the expensive part. If I wanted the LED to be bright I would use a transistor or a dedicated chip to drive it. With that approach you can run the LED off the raw power supply and use a bigger dropping resistor. That gives you more latitude with the LED and there is less chance of damaging the expensive part by over stressing the output.

If you are driving the LED from a source with very low internal resistance, then the LED will be sensitive to small changes in supply voltage. If you are driving the LED from a large power supply capable of delivering in the amps range, and it drifts 10mV higher, you may cook the LED.

Note that in many instances, such as inexpensive flashlights, the LEDs are seen as disposable, and they are pretty sure the battery terminal voltage is not going to be more than whatever is normal for that type of battery's chemistry; the LED probably operates over spec or right on the edge with fresh batteries. Also, depending on the devices' forward conduction curve, you may not be able to get, say, 20mA into a white or blue LED on a 3.3V supply. And if you do the math, putting a 5 ohm resistor in series with the LED is not going to buy you a lot of voltage latitude.

However, up to this point we have only been concerned with the health of the LED, which seems kind of simple-minded. I would be much more concerned about over stressing one of the I/O pins on a microcontroller that cost me a few bucks than cooking an LED that can be bought for under 2 cents on eBay. So, if I were to connect an LED to the output of an expensive chip with a 3.3V Vcc, even if the LED was rated at 3.3V I would probably rather add a few hundred ohms and run the LED off just a few mA than risk damaging the expensive part. If I wanted the LED to be bright I would use a transistor or a dedicated chip to drive it. With that approach you can run the LED off the raw power supply and use a bigger dropping resistor. That gives you more latitude with the LED and there is less chance of damaging the expensive part by over-stressing the output.