I understand that the distribution of information is changing and that since they are a Twitter platform that they, "have PR covered" using their various social media platforms or possibly an agency, but what I didn't understand was why a small startup would not want to receive all of the free coverage they could get.

As a nonprofit executive you should not make the same mistake. Take every opportunity to promote your cause or the good work you are doing through any channel that is presented. These days it is vital to have a presence on most social media platforms to push your message out, we are on Facebook, Twitter and LinkedIn and are evaluating Google+ and a few other platforms, but media distribution is still your best bet when it comes to getting a message out to a large audience. Someone might stumble upon one of your social pages and become a supporter and it might go viral, but get mentioned on the TV, in a newspaper, on media website or email newsletter and you are reaching far more potential donors than most nonprofits social media efforts do.