On the contrary, my friend, the big companies hand out interviews like candy at halloween. Getting a job offer, on the other hand, is where the trick lies.
I couldn't have done it, not for visa reasons, but for not-being-in-the-country reasons! I'm only in America for a short time (which is coming to an end in a few weeks) before I go back, and I just applied to the big companies as a crapshoot to see if I could get a better gig with any of them. No such luck.