The reason is: (Answered by Hugh Wright from /n software)
There are several potential causes for this error. Previous users who have had similar errors fixed it by changing the depth property of the WebDAV component. By default, the WebDAV component uses a depth of infinity when calling certain methods, including FindProperties and ListDirectory. Some servers do not support requests with a depth of infinity, and may return a 403 error when the request is made.
Webdav1.User := 'username';
Webdav1.Password := 'password';
Webdav1.AuthScheme := authBasic;
Webdav1.Depth := dpImmediateChildren; // The server will operate on the
// collection resource URI and all of
// its immediate member resources (but
// on none of their member resources).
Webdav1.FindProperties('ResourceURI');
I was able to confirm that the issue was the Depth Property. By default, CarotDAV uses a depth of 1 (Immediate Children), and our component does not.