@pleonasm - I think any company which had a dedicated travel secretary would have to have employees who were used to traveling. It makes me think of that film "Up in the Air" where the employees were sent all over the country to perform their job.
They would almost certainly need someone to be booking their flights and hotels and making sure that they get to each place in time.
And they would almost certainly know that travel isn't always going to go smoothly. I mean, I think that's just part of the job as a travel secretary. They'd call if there was a problem and she or he would have to sort it out for them, or at least try to.