That being said, what's more important is you're good at what you do, that you can back that up with examples of work, projects worked on. So it's always good to network, create projects (even for fun) to help accumulate your body of work. Back when I was at school social media was only facebook and only for socialising, now (especially with instagram) it's so much easier to create an online portfolio of your work. Or even if you create an account just about film production or films you love and that gains a good following, then eventually you can put your own work on there
Overall, it doesn't matter if you go to an amazing film school or a normal one. Plus sometimes you don't even need to go to film school to get a job in film. For instance, I studied Journalism and was still able to get a job in feature films. In my experience, I would say USC is the best film school - I know several alum that have very successful positions in production and at major studios.
Many people wanting a career in film typically start out as a Production Assistant and that's where you'll learn a lot. Plus this will be where you make the connections needed to excel in a film career. It's not just about what you know, it's who you know. Many films wind up hiring the same crews over and over again because there's a level of trust there - so be sure to make a great impression and keep in touch with everyone you meet.
Best of luck!
You definitely don't have to go to a big name school to get a job in the film industry and depending on what you want to do you may not even have major in it.
Some perks about going to film school is that they will provide equipment, access to industry standard software (like AVID), and networking events with alumni and/or guests your teachers invite. Many film internships require that you be a university student to qualify. A few of my classmates actually got hired after their internships at NBC and Dreamworks.
You should also look into schools thats offer programs open to all majors so you can still study something different while gaining film experience. One of the editors at my alma mater's student-run production company was actually an Econ major who learned how to use Adobe Premier through tutorials. And my friend who studied history made a short with the school's film club that got into a few festivals!