Yes, I agree that the SOPA petition did not change the White House's mind on DNS. But it did provide a good PR hook for them to put a stake in the ground, and clothe it in the veneer of public support.

It's probably best to think of the petitions as a PR tool, not a policy tool. Getting a petition over the signature threshhold, or getting a response, is a great news hook that activists can use to generate press coverage of their issue. For example: this discussion would not be happening today if this response had not been issued.

It's also possible that a petition can help affect policy over a long term. In general, people outside of government greatly underestimate just how long it takes to go from an idea or complaint, to a policy shift, to a change in the law. It's not uncommon for it to take a decade or more. For example Silent Spring was published in 1962, but DDT was not banned in the U.S. until 1972.