A lot of the time they just ignore Twitter in case of hackers. Someone hacked into Amir's Twitter and contacted Jagex for the account login, Authenticator included. This happened recently and Jagex gave out the login, allowing the hacker to access the account through Twitter. Only took a matter of hours then for the hacker to get past the bank pin and into the bank (worth about 35B). I wouldn't be surprised if Jagex have picked up their game since then and become more strict ('social-media-wise').
Edit: Worded that^ very badly, hope I get the message across.