I never understood why people cared so much about company "name" until a handful of years ago. It's not about "status" in terms of what kind of fancy clothes you wear, but it absolutely signals an ability to clear a certain kind of bar, produce a certain kind of work, and experience things on a scale that you wouldn't at a smaller shop.
It doesn't mean one path is right or wrong for a job (I know many people who switch back and forth between bigcorp and startups), but if you only see BigCorp experience as status seeking/soul sucking experience, you're missing a huge part of the picture.