According to After Elton, the Inaugural Committee is saying they never told HBO not to broadcast Gene Robinson’s prayer and that the whole thing was an unfortunate mis-communication. 

The Presidential Inauguration Committee just issued a statement saying, "We had always intended and planned for Rt. Rev. Robinson’s invocation to be included in the televised portion of yesterday’s program. We regret the error in executing this plan – but are gratified that hundreds of thousands of people who gathered on the mall heard his eloquent prayer for our nation that was a fitting start to our event.” — PIC communications director Josh Earnest. 

Okay…  So why was the Gay Men’s Chorus closeted?