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?