It's not that they don't believe you, it's in their protocol to blacklist if there are 3rd party applications running on your computer. You also have to think of their position, they're giving you an interview, and they ask or question or you give an answer or whatever and dicord pings are going off. If you maintained your innocence in the interview, you could have put in an appeal, explained in full detail what happened, say it won't happen again and see if there's any arrangement you can make to be able to take your test. Instead, you went to forums and made it public trying to get support from the community, but the community doesn't decide who's cop, the senior APD does. So you shouldn't have went to the forums, you should have went to support. But now you put yourself in a worse position, by going to the forums to publicize this, senior APD might trust you even less or feel you are more of a pain than you're worth i.e. the title of this post.
Edit: I've had lots of experience with getting blacklisted, on both APD and R&R, and have found in all my cases that shit posting on forums has never helped the issue be resolved.