I agree, it's the radio. They need to fix it. I remember Mr. New Vegas annouced something (which now I've forgotten) that has never happen yet.
If you wipe out the NCRCF without following the powder gangers leader Eddie's chain of quests the radio will not tell you the prison has fallen to the attack.
Otherwise it should work fine, but sometimes the radio takes a bit to adjust.
Did you kill everyone in all the buildings apart from Sayer?, that may have been the issue idk though for a fact however.
Then I'm on pc so the X Box might just have a unique bug.
Edit: Go for the eyes boo!, go for the eyes !!!!!