My room is 400 square feet, but we’re being told to order 450 square feet of flooring.  Is this really necessary?

Yes. As a general rule, you should plan to order 10% more flooring than is needed for the installation.  Much of the material will be cut to fit the exact space, and once the boards are cut, they likely cannot be used elsewhere in the room because the end tongue or groove will have been removed. Once that happens, that board can no longer adjoin with another board, so there is some waste involved.  

You may need to order slightly more or less depending on the room. For example, if you need to work around stairs, a bay window, a fireplace, and a closet, you may need to have more than 10% overage, but if the room is square with no interruptions, less than 10% may work. Your contractor is your best resource for helping you estimate the material that will be needed to complete the job.