Character mistake: A space traveler would not be "going to Orion." The major stars in Orion vary in distance from the earth from 243 to 1,360 light years. Orion is only a constellation as visible from Earth; once you get away that far, the stars would not be in the same alignment as they are from Earth. They would have been going to a specific star, probably Bellatrix at 243 light years, as Taylor mentions being at 320 light years.
Suggested correction: I'm not sure what scene you're referring to, but I never heard anyone say they went to Orion. Taylor says they're on a "planet in orbit around a star in the constellation of Orion. That could be Bellatrix." To Taylor, who is from Earth, the star is still in the constellation of Orion.
I agree with your take, but I still think it could be interpreted as Orion's stars all being in close proximity. And I would hope they would know about the 320 - 243 light year issue.
