Incorrect:
If you use a Master's Datacron, you can use THAT character to start the Story from the beginning, ( or carry it on from whatever level you used it on.
It is the Outlander Character Token that will not allow you to do Story.
Partially incorrect, you can finish earlier than level 60, depending on what you do on your journey.
To get Legendary Status credit for a character, Chapter 3, it ends on Corellia.
The FULL Story ends on Ziost, which is the question that Semiramis was answering.