Whether it was mind games - or good, old honest respect for the opposition - McCullum perhaps elevated even the admirable Cook above his station. Cook, England's all-time most prolific Test centurion, followed a rare first-innings failure in Dunedin last week with a 24th hundred second time round to help complete the tourists' fightback and secure a draw.
Asked how the Kiwis can hope to dismiss Cook in the remainder of this series, McCullum said: "I think we bowled reasonably well to Cooky the other day. He's obviously a genius batsman - his record is testament to that. Where he is at in his career at the moment, he's as good as anyone who has played the game - probably barring Bradman."
Cook, an ever-present for a record 87 successive matches for England, is in his prime at 28 - and his aversion to unforced errors makes him a formidable opener.
"He's enjoying the captaincy as well and leading from the front," said McCullum. "We just have to bowl areas where we think we can dismiss him.
"If he's good enough to overcome that, then so be bit - and you move on to Plan B."
Bradman's unfortunate opponents doubtless went through many of the same thought processes, to very little avail. But McCullum's high praise for Cook still does not quite stack up.
The England captain's average of 49.60 is just under half Bradman's peerless 99.94. Between the two are another 38 batsmen in Test history with higher averages than Cook's, including eight present-day players and eight from his own country through the ages.
Among those above him, in terms of runs per innings, England's Test match coach Andy Flower comes in at 51.54 - while Cook's team-mates Jonathan Trott and Kevin Pietersen are just a fraction below their captain. It took a moment for the man himself to recover the power of speech when told how highly McCullum rates him.
The best he could then do was to try to return the compliment for an opponent who is no slouch himself: "It's very nice of him to say that ... I'm not quite sure where he's got that from. You could talk about his genius batting, the way he hits the ball sometimes."