Some terrible reporting as per usual so it's hard to get to the truth. The current round of "hero" pilots BS would be pretty embarrassing for the crews and I feel for them at the moment. Sydney's wonderful Daily Telegraph (!) seems to think there's only 1 pilot on each aircraft as there are only 2 "smart" "hero" pilots apparently.
It seems the aircraft at 38,000' "asked permission to rise" (DT words!) and I'm going to say that was to 40,000'. With the opposite direction at 39,000, this created a conflict that the TCAS identified and resolved. The actual distance of separation is fairly irrelevant. It will be interesting to see which flight director mode the climbing crew used as this would have had an impact on the actions of the TCAS system and may explain why only one gave a resolution advisory.
At the end of the day, the controller made a mistake. There are systems in place to protect against that and it worked well in this case.