twitter_cron() breaks when there are no authenticated accounts

Repeatable: Always (three attempts)
Steps to repeat:
1. Upgrade Drupal Core from 7.14 to 7.17
2. Upgrade Twitter module from 7.x-3.0-beta4 to 7.x-4.1
3. Install Twitter library from github in libraries /sites/all/libraries/twitter/ directory
4. Install Oauth module 7.x-3.0
5. Run update.php
6.. Configure Twitter module with oauth consumer key and secret
7. Clear caches
8. Run cron from Drupal Administration

Expected Results:
Cron runs successfully and Twitter feed gets latest information

Actual Results:
After pressing the "Run cron" button, there is a ~2 second pause and then a white screen results. This error is generated:

Fatal error: Call to a member function user_timeline() on a non-object in /var/www/staging/sites/all/modules/contrib/twitter/twitter.inc on line 139

Line 139 in twitter.inc: $statuses = $twitter->user_timeline($account->id, $params);

Twitter feed does not update, and cron is not run successfully. With the Cron Debugger module, when cron is run with the Twitter hook disabled, cron runs normally. No error is logged, but the following message from the Cron Debugger module appears when the page is refreshed:

Cron presumably failed while running the cron hook twitter_cron() in the module twitter.

Note: When Twitter module was upgraded, it was not disabled first due to other module dependencies. The directory twitter was simply deleted, then the new version replaced it, and update.php was run. When Oauth was installed, it automatically was enabled. Also, here are the Twitter settings in the configuration:

Twitter host: http://twitter.com
Twitter API: https://api.twitter.com/1/ (also tried without the "1/" at the end)
Twitter Search: http://search.twitter.com
TinyURL: http://tinyurl.com

Oauth settings are configured with the dev.twitter.com, with the key/secret combination reset and re-input several times and the callback URL correct.