I can change the name, the default content, and input option values. I can't change anything else about it, and it must be available to any resource that I want to edit or create (default template). This is on the Cloud, so it's not a problem with mod_security. The MODx team is looking into it, since it started happening immediately after the paas2.ams server crash, and I'm pretty sure that deleting that TV was the last thing I did in the previous work session, so I can't say if it caused the problem before the crash. Maybe that's what caused the server crash
Ok, I solved the problem. I created new templates, with the same template content as the originals, and used Batcher to change all the resources to use the new templates. Then I deleted the old templates (changing my default template to be one of the new ones) and deleted the errent TV. Apparently it was something to do with the templates rather than the TV itself. Who knows? All is well now, so who cares?