1. Study of startup patenting in various industries indicating entrepreneurs say patents help getting financing: http://www.law.berkeley.edu/9135.htm
(There was controversy around this study, where VCs with an anti patent stance, such as Brad Feld, publicly disagreed with the analysis. As TFA shows, they are probably in the minority.)
2. Study showing startups with patents more likely to get late stage financing and/or have a successful exit: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=802806
3. Study (apparently -- it's paywalled unfortunately) showing startups with "stronger than typical" IP more likely to succeed: http://m.iam-magazine.com/blog/detail.aspx?g=ae1d78db-9c5e-4... (Note that the study was done by MIT Sloan and IPVision, an IP consulting firm, so something to keep in mind.)
Keep in mind that all studies must necessarily make some assumptions to make sense of their data, and some assumptions may be more valid than others. Also, different data sets and different methodologies give different results. For instance, the 2007 paper in [2] found much lower patenting rates in software than did the 2008 survey in [1].
Yet the patent possession/success correlation is hard to doubt. In addition to [2] and [3], there are other papers, such as by Rosemary Zeidonis, that also show a robust correlation between patenting and eventual success in high tech industries. Also, there's a working paper by a Pepperdine professor showing firms with patents four times more likely to succeed. I linked [2] particularly because it has a greater focus on the software industry.
I do agree that Twitter's strength is in network effects, and so is less likely to be affected by issues affecting other startups. Just trying to show some numbers to explain why (some) investors see the lack of patents as worrying.
However, the argument that the Innovators's Patent Agreement will attract the "best and brightest" is a false premise, handily disproved by Google and Facebook, just to pick two. It will attract a certain type of talent, maybe something Twitter is particularly looking for, but "best and brightest" is not necessarily it.