The White House Press Pool is an official institution that agrees to pool the resources of the five major media organizations, and then share the interviews with the other media in order to facilitate the White House getting face-to-face interviews done in a practical manner. The media organizations themselves decide who will make up the pool and Fox News Network has been included since 1997.
This pool is the representative of the American people and as such is not controlled by the White House. The President has no choice about which media organizations are included – that decision is made by the media itself.
When this president attempted to change the make up of the pool in order to punish Fox News for reporting things which the Obama adminstration did not like, they wanted to delegitimize the messenger in order to discredit the information.
President Obama can choose to avoid doing interviews on Fox, or not allowing his staff and other administration officials to appear on Fox – but he cannot try to strong arm the make-up of the official press pool.
Yes, this is an attempt to restrict the freedom of the press, and it is a well known technique by community organizers to boycott what they perceive as unfriendly media. This is a tactic that Obama learned from Saul Alinksy – and one that while useful as a community organizer has no place as a tactic now that he is president (of all the people, even Republicans) of a democratic government.