Those on a mobile device that is sporting the Twitter app are always welcome to use that instead. But if you need to quickly check out a tweet and you're using someone else's phone, your best bet is to use the web and open the mobile Twitter website. It would seem that Twitter is also hoping to gain new users from those who have never signed up for an account.
For example, if a person who is not a Twitter user scans the number of tweets relating to a subject, it might get he or she interested in opening a new Twitter account. Or, if someone without a Twitter account is so enthralled by Twitter that they want to post a message or reply to a tweet, they are going to have to open a new account to do so. The "logged-out homepage" allows users to only read tweets while not signed in.
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