According to the Jezebel article and wikipedia most revenge porn photos are selfies or photoshops of stolen non-nude pictures. In which case copyright law would apply.
However, to answer your question, you do own the copyright of a photo you take (unless it is a work for hire) even if you take it without permission. The requirement to get permission isn't related to copyright, it's related to the right to privacy. People have sued for damages over revenge porn violating their privacy rights.
http://www.scribd.com/doc/138909420/Revenge-Porn-Complaint-H...
If you think in terms of rights to privacy, then it becomes a lot less fuzzy. A child playing in a public place has no expectation of privacy regarding a photograph being taken and put in a newspaper. When someone lets a lover take photographs of them naked there is an implicit expectation that those photos will remain private between them. It would be hard for the photographer to argue that there was no reasonable expectation of privacy when the purpose of distributing these photographs is to get revenge.
However, to answer your question, you do own the copyright of a photo you take (unless it is a work for hire) even if you take it without permission. The requirement to get permission isn't related to copyright, it's related to the right to privacy. People have sued for damages over revenge porn violating their privacy rights. http://www.scribd.com/doc/138909420/Revenge-Porn-Complaint-H...
If you think in terms of rights to privacy, then it becomes a lot less fuzzy. A child playing in a public place has no expectation of privacy regarding a photograph being taken and put in a newspaper. When someone lets a lover take photographs of them naked there is an implicit expectation that those photos will remain private between them. It would be hard for the photographer to argue that there was no reasonable expectation of privacy when the purpose of distributing these photographs is to get revenge.