Most led's run off of about 1.2 volts & always some sort of current limiting resistors in series with them. I have to assume that is what Ratshack did with those leds.
If they didn't, then that is why you're measuring such low resistance across those leds as they are probably shorted now. In fact if you are using the diode checker setting on your meter, they should only read one direction & then only around 1.2v drop in the one direction.
I'm not certain about how the switching works on the bandit, but it might not be able to correctly power the led's without affecting the switching circuitry, in other words, they led's themselves might be enough to keep the feature activated even when the led is on.