I don't buy the "we're a poor non-profit" bit that people keep attributing to Mozilla - did they ever say that? Their income in 2009 alone was over $100m, pretty much all from google. I can believe it's an ideological stance though.
Digging deeper, it does seem the non-profit excuse has been tacked on by supporters and others, but not directly by Mozilla. I found
this article from Robert O'Callahan, and it's all an ideological stance as you suggested. It looks like the Mozilla Foundation is the non-profit portion, with that organization owning the taxable Mozilla Corporation (Firefox) and Mozilla Messaging (Thunderbird) organizations.