Todays thought is a spectacularly obscure “feature” in Microsoft’s IIS 7.0 web server. Credit to the Mindtouch Developer portal team for this one.
To fix the 405 error, go to the root of your site in IIS, find the Modules button and double click it. Scroll down to WebDAV and hit Remove on the right. Back out and open up the WebDAV feature options. Make sure it’s disabled (you’ll have the option to enable it on the right). You might want to clear out any Authoring settings you have in there as well, just to be sure.
Who would have guessed?