The shock jock appeared to link his view — that Castle's administration doesn't understand the real issues Australian rugby is facing — with the copy Newman produced for the official match-day magazine.
Other commentators believe Jones' attack on Newman was motivated by other factors.
Jones wrote in his regular column for The Australian that Newman was a "paid mouthpiece" of the ARU.
"I picked up the rugby programme for the test match last Saturday in New Zealand," Jones wrote.
"The world of rugby was present at the game. They would read the programme. And some hack, Beth Newman, is writing on Australian Rugby. You guessed it — she's a paid mouthpiece for Australian Rugby.
"How the hell would her utterly irrelevant musings represent an appropriate evaluation to the world of the state of the Wallabies? And what on earth must the rest of the world think about us when such drivel passes for authoritative comment."