BNA Radio is the one who probably should have the most Situational Awareness of local geographic features as well as RNAV points - the operator should have been aware of the potential conflict.
Why? He hears (maybe) someone broadcast to LIS traffic that they are just to the east of LIS and descending. That tells him nothing. It wasn't directed at BNA Radio. Is he supposed to jump into any obscure broadcast in a large shared CTAF that has 3 busy aerodromes in it to query everyone? One of the complaints about the CAGRS is that it causes extra frequency congestion. You want even more? There was only 4 minutes between the Jab broadcast and the near miss. Give it 30 secs for the actual broadcast and that leaves 3 1/2 mins for the CAGRO to respond, get the Jab to answer, have a to and fro with the Jab about what he is doing, where he's going etc, assess that against the A320 and advise them. I'd reckon the crossing would have occurred before anyone worked out where everyone was. That is if the CAGRO is not dealing with the local BNA situation (which is what he's paid to do). We don't know what other broadcasts or discussions were happening on the CTAF, or between who. He only had to be looking out the window and see someone start up on the apron and his attention is diverted to the local situation. Saying he should have been aware of movements outside his sphere of influence is a long bow. He's got no surveillance capability except his eyeballs and a radio and I doubt he can see 12 miles.