After working on this further, it appears you couldn't be more wrong.
So for those who may be reading this in the future, if you'd like to use HTTP Basic Authentication, just pull out the Fetch from URL module, click the down-arrow in the upper right-hand corner of it, and check the box next to 'HTTP Basic Auth'.
Similarly, for custom HTTP headers, there's also an option to check for that ("Custom HTTP headers").
Admin, if you don't know the answer to something, just say so (or hire someone who does). By leading people to believe the answer is simply "no", you make your product (you know, the one we're paying thousands of dollars to use) inferior by leading people to believe that functionality doesn't exist when it really does.