Does he need permission for something that was public (Assuming it was public on another website)? If this was the case he didn't break anybody's privacy. Just saying.
Permission. That's debatable. Considering a few things: that what he posted is publicly available to all registered users, that he is not the owner of the website who should be the determiner of posting policy, and that it's not prohibited for DSiPaint users to screenshot content on this website and circulate it.
I doubt it would be considered plagiarism seeing as DSiKlub does not appear to own a legal copyright, if they did it probably would not apply to collabarative user-created content, and the only restriction that the owner maintains is for users not to copy source code.
Once a website is made and it is "fixed in tangible form" (accessible/observable in any form), it automatically receives a default copyright (regardless of whether or not the owner decides to post a notice on his site) that protects all visible content and graphics. This means that other individuals may not reproduce the content without the owner's permission. It gets admittedly sketchy when user-generated content is introduced. To go further with a copyright document specifically detailing what should be protected, it usually costs money.