Incorrect. Rested experience only affects the killings of NPCs, double XP as a part of this promotion affects literally everything (space, quest rewards, PvP, etc). Technically, this double XP is way better than what you would normally get from rested.
So essentially, these Double EXP Weekends spread the effects of Rested EXP to all activities instead of just killing mobs, but you will not run out of Rested EXP. Did I understand this correctly?