But Max, 18, posted a photo of himself with Mr Obama on Facebook with the comment: "Cheers for the round Mr President."
What's it like playing golf with the most powerful man in the world?
"It was like being on the golf course with a couple of mates," Mr Key said today.
"There was a lot of laughs, a lot of fun, five hours of discussion - which was everything from family and social right through to obviously business matters. But it was a unique and great opportunity for us."
As for who won, Mr Key diplomatically said that he and Mr Obama were on the same team.
"He played really well, I can say that."
The golf outing put Mr Key in rare company. Mr Obama is an avid golfer but prefers to limit his playing partners to a close circle of friends and advisers.
Among those who have also scored invitations to play with Mr Obama in the past are former President Bill Clinton and House Speaker John Boehner.