Learn English – What does “cock-back“ mean

I think you are right; it refers to American support either for Mubarak or his opposition. Her phrasing is a bit odd, but I'd interpret it like this:

• backing = supporting
• back = those who want to go back to the old situation, Mubarak in power
• forward = those who want to go forward to a new government

"We do not want to send any message [to either party] about [our] supporting those who want change or those who want to go back to the way things were."

In the 1960's, some music groups recorded tracks on songs that sounded like gibberish, but, if the record was played backward (remember, these were vinyl records, so you could place the record on your turntable, and the needle on the record, and turn the record with your fingertip), the gibberish would become ungarbled, and a clear message could be heard. (This is called backmasking.) Perhaps the most famous of these messages was one that said "Paul is dead" on the Beatles' song Number 9. (This example is so popular, you can still buy a T-shirt.)

Country music is known for lyrics where songwriters lament about things that are lost (lost loves who have walked away, lost fortunes that have been squandered away, etc.). David Allan Coe even made fun of this, in a way, at the end of his song You Never Even Called Me by My Name:

(spoken) Well a friend of mine named Steve Goodman wrote that song
And he told me it was the perfect country and western song
I wrote him back a letter and I told him it was not the perfect country and western song
Because he hadn't said anything at all about momma or trains or trucks or prison or gettin' drunk

(still spoken) Well he sat down and wrote another verse to this song
And he sent it to me and after reading it I realized that my friend
had written the perfect country and western song
And I felt obliged to include it on this album
The last verse goes like this here

(sung) Well I was drunk the day my mom got out of prison
And I went to pick her up in the rain
But before I could get to the station in the pick-up truck
She got runned over by a damned old train

So, put those two things together – backmasking, and recurring themes in country music – and you should be able to understand the joke.