One caveat is that Twitter is not actually a revenue-producing concept :)
However, a well documented example of such a process does exist: Google. In the first paper they published about the search engine, then an academic project, Brin and Page explain that one of their goals is to provide an alternative to commercial search engines:
Currently, the predominant business model for commercial search
engines is advertising. The goals of the advertising business
model do not always correspond to providing quality search to
users. ... For this type of reason and historical experience
with other media, we expect that advertising funded search
engines will be inherently biased towards the advertisers and
away from the needs of the consumers.
...we believe the issue of advertising causes enough mixed
incentives that it is crucial to have a competitive search
engine that is transparent and in the academic realm.
(from http://infolab.stanford.edu/~backrub/google.html#a)