おる is a less common variation of いる. While I do not think that it is incorrect, I do not know why the quoted sentence uses おれば instead of いれば (or おけば as Hyperworm suggested).
大手を振る (sense ) describes how a person behaves proudly (without being ashamed of anything).
I would translate
A world where they can live without shame while they fake facts and do things which seem to be against ethics given the responsibility of mass media, as long as they have a high audience rating
I have to say that the translation into English which you quoted is sloppy. Where did メディアの責任 and 大手を振る go?
Moreover, just in case, I recommend you not to consider that the quoted Japanese sentence is well written. I think that it is written carelessly for at least the following two reasons: (1) it is unclear who is thinking in メディアの責任を考えればモラルに反すると思う; (2) やらせ is apparently one of the メディアの責任を考えればモラルに反すると思うこと, and therefore listing these two in parallel does not really make sense.