Possibly, but Turnbull did take over as head of https://murdochroyalcommission.org.au/ after K Rudd stepped down to take whatever diplomatic job it was he took.

I think the Murdoch press had a big hand in Turnbull being replaced as PM, because he was actually considering implementing renewable energy policies https://www.theguardian.com/australia-news/2018/sep/19/turnbull-warned-rupert-murdoch-trying-remove-him-prime-minister

That same day the Daily Telegraph had warned of “a toxic brawl” over energy policy. On Sky the night-time commentators Peta Credlin and Andrew Bolt ramped up their negative assessments of the national energy guarantee and of Turnbull himself.

So he is probably butthurt for other reasons too