Speaking to Test Match Special shortly after play, McCullum said that relations between the sides would become strained. "I can't imagine we'll be having a beer anytime soon, if that's what you're asking," he said. "From our point of view, we've got three Test matches to try and land some blows and try and win the Ashes and that's where our focus will be."
When the comment was relayed to McDonald, he said: "I haven't spoken to him, [have] heard that comment for the first time, and somewhat disappointed by that."
In contrast to McCullum, England captain Ben Stokes, who scored a magnificent 155 to put his side in with a chance of a remarkable victory, hoped that the dismissal would not cause rifts despite the difference in opinions between the two sides.
"I think there's a bit of emotion in that, to be honest," he said. "It's very soon after something happens. I'm not one to hold a grudge too much. I've been through enough to know you can let things go. But I think to ruin a tradition that's been so long, such a big series, I think the feelings from a few people will definitely change as the series goes on.
"Maybe if we weren't to do what we always do and have a beer together and say well done, great effort and all that kind of stuff it would be sad. But I think that was just emotion."
McDonald, meanwhile, did not see the Bairstow stumping as any different to other forms of dismissal when a batter was out of his ground.
"There's no doubt when a player is leaving their crease or leaving their ground at certain periods of time that you take that opportunity," he said. "It's [the same] with every player. It's like when a player is running down the wicket to Nathan Lyon, does he take the opportunity to fire a ball down leg side, because he's leaving his crease? There's no doubt about that. You see a run-out opportunity at point, you throw at the bowler's end.
"But any of these events are always going to polarise opinion," he added. "We saw it on day four with the [Mitchell Starc] catch as well. Some people thought it was out, some people thought it was not out… sometimes, you know, not everyone agrees with it."
Away from that moment, McDonald was delighted with how Australia had put together their performance, which he felt often saw them with the tougher end of conditions - batting under a cloud cover and bowling with the sun out. The twin half-century opening stands between Usman Khawaja and David Warner were key in putting Australia on top.
"I thought the way that we were challenged on day one with the ball from England was what we'd call the most conventional Test cricket," he said. "There were overheads and the way that we played on day one to set up this game.
"I think in some ways that conditions almost conspired against us at certain times. It seemed like every time we were batting, there were overheads and lights were on. And our ability to be adaptable through that period and navigate our way through was outstanding to give us an opportunity to set up the game the way it unfolded.
"So really proud of the way that the boys have gone about it, and it seemed on the opposite end, when we were bowling, the sun was out… hopefully we get on the right side of those conditions at some point in time."
"We like to have a spinner in our attack," he said. "And as you saw [on Sunday] at certain times we had to do it differently without Nathan down the other end which we've been so used to. At times it looked a bit chaotic so we do like to have that spin option."
Andrew McGlashan is a deputy editor at ESPNcricinfo