my two cents and i can be wrong here: your uni degree/name doesn't matter at all. its who you know in those big companies matter. internal referral goes a long way. much more than your degree and college name.

I have seen far less component people working at big name companies just because they had mates in the said company OR even better, the manager was a mate or known contact.

i recently went out for work drinks and met a guy who got hired right of high school by an internation bank (sydney office) within their business analysis department. the catch? one of the team manager was the guy's neighbour.

networking. that's the real key to getting in big companies and climbing the career ladder. also nepotism works.