It isn't your money, so it isn't your call. If you don't like it, ask to see the travel policy as you interview somewhere else.
In addition to the above, it is quite common for Concur (or similar) to be set to log any selection of a fare higher than the lowest available. IOW: It doesn't matter how you run your search. If there was a lower economy fare available on any flight within some hours of your departure, then your decision to pay a higher fare (and the $ difference) can be logged and reviewed at any time in the future.
A travel agent who is applying specific fare basis codes for this purpose is also risking his/her job.