Is working for a big corporation invariably wrong livelihood? That can be a very complicated point.
Almost every work for a big corporation could be (potentially) seen as wrong livelihood! Hard to find a big corporation that works with good products, ethical conduct, respects the environment, the employees and is not involved in tax evasion, bribe or any other scandal... so what is more important from a Buddhist's point of view: What YOU do in your work routine or what your company does or sells?
It does feel like big corporations are somehow less ethical but I suspect it's related to complexity. In a smaller company it's relatively easy to understand whats going on and where the ethical grey areas may or may not be. I work in a company of 30 people so I've a reasonably good idea what we are up to and if there are any major ethical concerns. However in a bigger company all manner of things can and will be going on. Your department may be perfectly ethical but another department might be selling arms to unsavoury regimes. The office 50 miles away might have real issues about work place bullying. The executive board might be engaging in large scale tax evasion. In a big company there are a lot of conditions in play, lot of things going on, lots of places to hide. There is bound to be good and bad there.

But in reality we are all affected by each other. A small company has suppliers - what are they up to? A small company invests in pensions - is it ethically investing? A small company still has an environmental footprint - is it excessively flying its people to other countries? The more we think about ourselves and others, the more these issues will come up. I think we are living in a golden age for Buddhist practice (controversial I know) but I do think that our livelihood is one of the areas that is more difficult for us in the modern world. But we still need to consider this kind of issue - exactly as you are doing.

I've a personal preference for working for smaller companies but I'm not sure that it's because of right livelihood and general ethical concerns. It might be just my ego playing out - preferring to be a bigger fish in a smaller pond.