Anonymous users cannot upload a file

Adding a file field to a webform doesn't work for anonymous users. On form submission, the following error occurs:

 PHP Fatal error:  Cannot unset string offsets in /var/www/sites/powerofacting.org/includes/form.inc on line 2157

The error occurs in form.inc in form_state_values_clean(), and it looks as if the form value for the file field is not in the expected format.

Registered users don't get this error.