I'm still confused...
If i'd measured the battery to be 4.2v, I would have put a series resistor in. I measured the battery at 3.37v, which i knew to already be less than the forward voltage of the LED, so I saw no harm in powering the led from it for a moment or two.
You keep harping on about the battery at full charge, BUT IT WASN'T! The battery I used was at 3.4v. Please tell me what resistor makes sense to use when powering an LED with a forward voltage of 3.8V in that circumstance. Someone said earlier that they were surprised the LED fired at all, so why would I have put a series resistor in, AT THAT VOLTAGE?