I love it when people try to "explain" time travel. It always comes off so convoluted and ignores too many vital pieces. This is why, in retrospect, i'm not so disappointed in the Stranger's reply of "no time to explain". They almost did us a favor by not having her explain Destiny's version of time travel, as it's bound to either be silly (like this idea which still doesn't excuse paradoxes) OR it's bound to be convoluted (like any compelling time travel story).
Time traveling is NOT the most interesting thing about Destiny's lore, for all the right reasons. If it turns out to be too pivitol in the story arc, this weakly built universe will crumble into a steamy, steamy pile.
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How would there be a paradox? This is a perfectly possible thing. The vex hide in the veil. Crota opens a hole into it. vex carry knowledge from previous timelines to do better in the next. There really isn't even time travel, it's just timeline hopping.