Is the use a very small value resistor negligible?
It means that you're using a voltage source which is too close to the forward-drop voltage of the LED. The problem is that the values are never exact. You may have a really fresh battery which gives out a bit more voltage or the actual forward-drop of that particular LED may be a bit lower. In this case, you will burn out the LED.

Conversely, the battery may be a bit low or the FD a bit high and the LED may not light.

You can't just use a 1.5 V battery to run a 1.45 V LED. The only case where you can really get away without a significant dropping resistor is where your voltage source has a high internal resistance which acts as a dropping resistor. This is used in the cheap keychain flashlights that connect an LED directly to a button battery. That battery has a high enough internal resistance that the LED never gets too much current.