I see it in my mind's eye, as you see it in the opening movie, when the Roegadyn Archetype physically stands over a downed comrade with his shield high. So in my mind, the mechanic certainly should be short range, but also it ought to use the Paladin's defense/parry/mitigation because it's the Paladin physically shielding the person they're Covering.

I am certainly going to find a place I can experiment with using Cover now!