The gulf between Australia and England over the stumping of Bairstow at Lord's has continued in recent days, with Stuart Broad highly critical of his Ashes rivals in a column.
England's main issue has been that they believe Bairstow thought the ball was dead at the end of the over when he wandered out of his crease and was stumped by Alex Carey.
But Australia have continued to defend the dismissal, noting that Carey immediately threw the ball after catching it given Bairstow regularly walked out of his crease after deliveries.
The Australians have also pointed to evidence of Bairstow returning the ball at the stumps while keeping, a point contended by captain Ben Stokes earlier this week who argued it was different when done mid-over.
But Head has now stated that Bairstow threatened to stump him at the end of an over in the first Test in the exact same fashion, and that he immediately raised it with the Englishman amid protests about the dismissal at Lord's.
"I reminded Jonny last week I walked out of my crease at the end of an over," Head told the Willow Talk podcast.
"I quickly whipped my bat back and questioned Jonny on whether he would take the stumps and he said, 'Bloody oath I would', and ran off.
"I reminded him (of that). Whether he remembered saying that or not. Two days before he also tried to throw Marnus (Labuschagne)'s stumps down too."
Head also questioned whether England would have withdrawn their appeal in similar circumstances, after both Stokes and coach Brendon McCullum said they would have.
"I know they've questioned it differently if they were in the same situation but with all the heat out of the air, saying that is a little bit different than in the moment," Head said.
"There's been some in the past when (wicketkeepers) have held the ball and waited for someone to lift a foot.
"This was purely in the same play. It wasn't sneaky, it was done pretty quickly. It left Alex Carey's hand straight away."
