You can pull down images with PHP if that will work for you. You just need to make sure wherever you are "Putting" the images, needs to have the write permissions.
I got the following snippet of code to work on the image url you placed above.
// Remote image URL
$img_source = 'https://res.cloudinary.com/demo/image/upload/w_400,h_400,c_crop,g_face,r_max/w_200/lady.jpg';
// Image path
// the tmp/ folder needs to have the correct write permissions.
$img_path = 'tmp/lady.jpg';
// Save image
$results = file_put_contents( $img_path, file_get_contents( $img_source ) );
// returns the number of bytes that were written to the file, or FALSE on failure.