Fox News had this story online yesterday. The couple charged had been on Drury's Dream Season and a couple of the kills charged appear to match the timeline of the show. Charges were rendered because it appears they did not purchase a hunting license before taking the bucks in question.
As for determining what's legal for transport in your state, a quick call to your fish and game office should clear that up. I might also advise doing the same for any other states you transit on the way home, just in case you get pulled over.