Previously you were able to add Twitter as a network without giving your password to us (and this was the only option for a little while), however, this is now no longer possible due to this change in the Twitter API. Twitter will now will require authentication before you can use it. Currently the only method of authentication for Twitter is a password (Twitter say they are working on supporting oAuth in future).
We now fetch all Twitter information using your username/password and this counts against your per-user limit of 100/requests per hour (currently) and this limit is shared with other sites that also take your Twitter username and password.
We are looking at ways we can enable users to follow a handful of users if you don't have a Twitter account.