“With all the supposed security, how do hackers get control of accounts on Twitter and elsewhere?”
They guess a password.
From Geek.com:
“Fox has already suffered two embarrassing hacks this year. The first saw details of X-Factor contestants leak including their full names, date of birth, zip codes, and phone numbers. Then LulzSec broke into a Fox database and stole a bunch of employee usernames and passwords. Today, there’s been a very public third hack that has seen the Fox Twitter account compromised.”