The Grimoire supports both.
Apparently The Traveler ran, but then "ran back" to aid Humanity.
But Rasputin stopped it from running away as well.
Maybe it tried to leave again and was stopped. Hence why its stuck hovering over the last city
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Its not clear at all , but from a moral point of view the theory of him trying to leave was never 1 i supported. It would make the traveller and humanity less special. I am convinced the Exos made the contingency plan ( in their moral weakness) but the traveller decided to stay and saw something special in humanity. The fact that this story was confirmed by Bungie supports my thesis.