I've never heard of Li-ion batteries damaged by running it until they were empty, I've heard the opposite, in fact, that it was better to do that so that you are not charging it as often. This advice comes from Radio shack vet of 20+ years of expeience, not myself.
20 years ago, they used NiCad batteries, and that was believed to be true, (disputed by battery experts).
However, todays cameras use Li-on, and a li-on cell will cease to be rechargable if fully discharged. There is electronic circuitry in the battery to prevent it from being fully discharged, but it is still not a good idea to run it down, because if unused for a while or freezing, the battery voltage may fall so low that it can't be charged with ordinary chargers.
"If overheated or overcharged, Li-ion batteries may suffer thermal runaway
and cell rupture. In extreme cases this can lead to combustion. Deep discharge may short-circuit the cell, in which case recharging would be unsafe. To reduce these risks, Lithium-ion battery packs contain fail-safe circuitry that shuts down the battery when its voltage is outside the safe range of 3–4.2 V per cell. When stored for long periods the small current draw of the protection circuitry itself may drain the battery below its shut down voltage; normal chargers are then ineffective.
Many types of lithium-ion cell cannot be charged safely below 0°C"