Sounds like it's a pretty high Vf emitter, although a high resistance somewhere else in the current path could have some effect.
http://www.candlepowerforums.com/vb/showthread.php?t=227147A P7 can be driven at or above the max rated current from 1 18650. The Vf is the biggest influencer of what the current will be. Was there any indication of the Vf bin on the LED you bought?