Well, that site only queries a database for the site you enter in the search box. It doesn't do a live real time scan. So I would have to use the client because their server more than likely wouldn't be able to scan my websites with me blocking certain things and many hosting providers like Rackspace, Digital Ocean, Amazon AWS, etc, etc.
But now that I think of it, I do recall seeing a CSS SSL something or other scan bot in my server logs a few times that got a 403.
If anyone wants to test for other vulnerabilities, check this site out.
https://www.ssllabs.com/ssltest/