Well, that's ironic. Considering that CF should be saving resources. (Already having issues with CF on a site outside this host.)
While I was away, I began thinking about what I've seen and how the scanner would work, I then realized that the scanner can be fairly heavy on resources (potentially triggering the high resource page) as it's looking in multiple directories and from the looks of the screenshot provided on the page, outside.
If the script is requiring you to change file permissions, then you should be able to do this either via file manager (cPanel) or via FTP client (which was said that the FTP accounts were removed, so that would be redundant).