My experience as a contractor is that, in addition to the ease of letting someone go cited elsewhere, it is very hard to evaluate a prospective employee, particularly in software development, by an interview. You can ask them the FizzBuzz question all you want, you can have them whiteboard answers and so on and so forth, but often all that brings you in is a person who has memorized a few programming tests and BSes well in interviews while leaving a more competent but perhaps less socially able candidate outside. And all the while, you have limited time in an interview situation - is there going to be time to judge if a candidate is competent and is a good cultural fit for your team?
What a contractor does for a large business is say to them "we have hired this guy out on other jobs and we think he is worth employing". Even if that information isn't 100% reliable (I have heard horror stories), it's still information that you can use and which most of the time is very useful. And if it does turn out that the guy was one of those BSing types, you can, as noted, get rid of them relatively quickly, and if they're bad in some of those horror-story ways I've heard you can choose not to do business with the contractor. All of this is information at your disposal that you simply do not have if you hire a guy off the street - if they're bad, there's no way of telling from that interaction whether or not the next guy is going to be as bad.
Also, my own gig, for example, is rather specific - I develop and administrate a specific piece of software - and IME there aren't very many of us in the country who can do this. As a large company, your choices are putting out ads on dice and so on and hope that you can find one of us, try to train up somebody from within (which can itself be problematic if you don't actually have anybody else there who can do the job already), or... hire a contractor that specializes in the specific thing that you need. I recently worked at a Fortune 50 company that, over the entire course of the time I worked there (a year and a half; since this company was partially based in California there were limits as to how long they could hire out temps), they had I think my boss said 4 qualified applicants interview (3 of us wound up getting hired). Not everyone is a generic front-end developer or whatever.