On one hand you don't want to remember multiple passwords (on multiple sites) and on the other hand you don't want to let people authenticate from your own trusted site.
Most of the time, since you are already logged-in on Facebook google, yahoo or twitter, you will not be prompted for password, only for approval of authentication.
Most of the time, since you are already logged-in on Facebook google, yahoo or twitter, you will not be prompted for password, only for approval of authentication.