Contradictions Removed
Here's an interpretation that reconciles the two sides:
Li-ion batteries indeed SHOULD NOT be
completely discharged. Well-designed devices will shut down to prevent a total discharge. Some charge will be lost even in no-power-used situations, so you might follow Apple's advice of connecting the phone to a charger, then shutting down the phone (leaving the charger going), if you're going to leave the phone for more than a few days, in which case you could otherwise completely discharge the battery.
The device software
can get confused about how much charge the battery is holding. Batteries are designed to have a constant voltage (1.5V for the AA's in your maglite), but voltage declines slowly when the battery has less oomph left. The charge indicator guesses from the voltage how much capacity is left, but it's a bit of guesswork-- the only way to know for sure it to drain all the capacity. So people often run the battery down so the device can watch the measured capacity versus OK, the phone actually shut down.
Because the phone protects the battery from total discharge, it does not risk the battery life-- that's down, not out. It DOES count as one of the limited number of battery uses that it'll deliver in its lifetime, so the increased understanding of your battery status had better be worth cutting its life by 0.2%. Once every month or two could fit most people's definition of that, and indeed, Apple has a battery info
page with a reminder reminder to re-calibrate their iPod or MacBook batteries once a month.
Note, the page does NOT specifically mention the phone; perhaps Apple has figured this is too much for your average phone user, perhaps they have some clever alternative so the meter shows more accurately what's going on, or even, perhaps, they haven't bothered to update it since the phone was introduced.
So no, do NOT completely discharge Lithium Ion batts, but YES, do completely use the available charge from time to time if your device is saying you're down to only, say 15% when you haven't really used it enough to justify that.