I tried editing another person's wallpaer tag and I could. Not sure whether it was done intentionally done but pls check whether the person who uploaded it , can only edit his/her relevant wallpaper tags,category etc...
It's intentional, someone may add a wallpaper without properly tagging it and someone else is able to tag those wallpapers. It's the community side of our website.
But only the owner and moderators can remove wallpapers, so don't worry for your uploads.