Naw, Fed Agents typically don't leak to the press on celeb stuff. Figure there's a civilian employee who sees the thing go down. He calls the local reporter, and the reporter calls the Feds, "Hey, I heard you just busted Rush..."
There's an entire economy based on celebrities...reporters regularly pay low level people for information on celebs. Fer instance, if you work for a nightclub and convince some A level celeb to show up and get their pic taken, it's worth a thousand bucks. Celebs, particularly rap stars, know this and leverage it.
Would Rush be detained or booked if this intitial story were true?
They had a lot of detail. For example, they knew it was over prescription drugs. The civilian employee would have had to be very closeby.
If all the TV station had was that "Rush Limbaugh was detained at airport. More at 11." I would be more inclined to follow your line of thinking.