Burke is pretty easy to understand, once you get the hang of him.
1. He's got a big ego, made almost insufferably so because he has a Cup on his resume. No problem there, many successful sports execs use that as an element of their success (though it should be noted that it's not a requirement, Holland, Poile, Rutherford, being good examples).
2. Like most people with egos, he likes to hear himself talk. There are 2 problems here: first, he literally doesn't know when to knock it off, and second, he constantly presents himself as a straight shooter, like he's being brutally honest 100% of the time. But like all of us, he equivocates, and exaggerates.
So when he comes out with patently absurd statements, some people are predisposed to believe him because he seems to be telling it straight.