So you're saying that some online petitions are actually meant to diffuse dissent about the thing they're petitioning? That would be a stroke of evil genius if it's true. Doesn't strike me as being the case so much as their being driven by naive idealism, but in the case of the whitehouse one, it's at least conceivable. In the long run, it's probably just going to demonstrate to a lot of people that online petitions are mostly counterproductive.
Online petitions exist to harvest email addresses so they can hit you up for donations and volunteering during the campaign. They're an easy way for campaign staff to build a mailing list of people politically engaged enough to be worth spamming.
All internet petitions are simply polls with identifiable voters, making their marks on a non-binding ballot. That petitions are portrayed as effective political acts causes people with only one political act in their schedule to waste their effort.