Every time you log in to a site with a password, you are sending your password server-side. If you don't trust the recipient, don't send your password. But sending passwords to trusted servers is a normal part of using the web.
Normal to get some service you desire. But this site is just collecting them, by their own admission. Its a little strange to assume folks will trust them, because they ask us to. Consider what a hacker would say to fool people? How similar to this site's message would that be? Identical?
Not on blockchain.info is not.
In this case Microsoft say their prediction database is too large to load on the client, which sounds plausible. I certainly wouldn't put a real password in there though.