Also I would have never been able get where I am today if I worked for a small business. Getting in with a national business is the only way to make your way to the next level of jobs, and continue to get promoted. You will get pidgeon holed if you start off at a small company, but it sometimes is a good spot to get some experience if you are looking to move into a big company.
Big companies do not hire more for specialties, of course some functions need specific knowledge but others do not. What matters is general knowledge and the ability to solve problems. The fact is that in the future, only the best will have the best jobs, so choose a good university and apply to make your efforts worthwhile in the future.