Based on what I know about Fort Greene PUPS, they at no point ever prevented a dog run from being built at the park. They have focused their energies on lobbying to make off-leash hours legal, installing a new (and sanitary) dog fountain in the park (which has just been installed! yay!), volunteering to beautify the park, supplying poop bags, being a source of information and networking between dog owners, etc. Point is, there's nothing preventing those who want a dog run to form a committee and trying to make it happen. There's a new dog run over in Bed-Stuy (on Lafayette and Marcy, I believe), and there's no reason why we can't have one, too. But, it won't magically appear.
If anyone starts a group up, I will post about it here. Just let me know. (My dog is kind of antisocial, so personally, we probably won't be interested in the dog run.)