In short, Burke is just answering honestly, according to canon law. In his memorandum entitled ‘Worthiness to Receive Holy Communion – General Principles,’ Pope B16 (when he was Cardinal Ratzinger) said without ambiguity:
“The minister of Holy Communion must refuse to distribute it [Holy Communion] when warning and counsel given to the manifest sinner have not had their effect.”
Neither Burke nor Benedict invented this as some kind of political novelty. It's the unremarkable enforcement of ecclesiastical law, which you can see quoted verbatim at post#7.
The only "remarkable" thing is how so few bishops bother to heed the law. That's been the shame and the bane of the Church for decades: long on doctrine, short on discipline.
I agree it was a baited question to begin with when he was asked. The reaction and answer was a for gone conclusion. He could have said no comment, but choose to again repeat is already quoted answer which was then printed calling attention, again, to himself.
There are many more Church leaders who would refuse to answer such a leading question when first asked let alone to repeat the same answer again.
But then again maybe the he likes to be quoted.
What seperates one persons “sin” being different from anothers is really the unanswered real question.