Plus in this case, the exception makes sense. Sure, you can't trigger your own healing surge while unconscious -- you can't do much of anything besides make Death Saves. Thing is, when the Cleric uses his Healing Word on you and triggers one of your surges, it's the Cleric doing the work, not you.
Think of it like this: you're someone with a heart condition, and you carry some nitro tablets with you in case of emergency. If you catch it soon enough, you can pop a pill under your tongue and probably stave off the worst. If you pass out, a bystander who knows what they're doing can either pop a pill under your tongue for your or perform CPR.
Those little pills are your healing surges. Of course, with D&D being a heroic game, healing surges are a tad more reliable.
And the paladin? He's the guy nearby who pulls a nitro pill out of his own bottle....