If you would like to prove otherwise, it can easily be tested, go find 3 dummies near each other, hit DS 1000 times and track how often it procs a HP then burn it on a WoG and make sure not to melee swing on the target, if you get less than say 450 (40% + 5% error) WoG it's definitely one per cast, if you get more than 734 ( (1-(1-.4)^3)*100% - 5% error) it's one chance to proc per hit. If you get in-between retest and average in the new results, and make sure to record the events.

To avoid the counter-argument of DS not being able to proc a HP when it hits nothing, this is simply due to the same fact that the spell fails to cast if it does not have an effect, such as before when it did not consume HP without actually hitting a target.

As I mistakenly did, anecdotal evidence counter to something widely accepted should only be brought forward with numerical evidence.