"Surely not - you have such a great shape already," they were saying as they played their part to the hilt.
The court announcer wanted to know if she needed a training partner.
Anna had her own lines down pat in her American twang.
The Miami-based Russian had, understandably, never heard of the All Blacks or Jonah Lomu a few days ago. By yesterday's centre-court interview, though, she had been charmed by the big fellow and would now be taking an interest in rugby.
Maybe it was pre-match nerves, but Kournikova was less charming barely two hours earlier when she snapped at a snapper.
As she crouched in the public lobby at the tennis centre in Stanley St, a photographer fired off a few shots.
Anna returned a verbal backhand that definitely wasn't a compliment.
Trying to work out these superstars is so confusing.
However, the pre-tournament publicity strategy is no problem to work out.
Beauty is in the eye of the beholder, as they say, and Anna is apparently an ad-agency dream - although I'm reliably told an Australian newspaper put some backspin on the Kournikova looks by running close-cropped face photographs of the tennis star and Boris Yeltsin that were hard to tell apart.
A bit cruel maybe, but then Kournikova has never been afraid to flaunt her looks, all the way to the bank.
The Auckland tournament certainly declared Kournikova a beautiful person.
Television advertisements portrayed the average bloke tennis watcher as having his eyes glued on, shall we say, to the Annatomy while the rest of the crowd swivelled their heads following the ball.
Us blokes are so predictable.
And the posters told us that tennis has never looked so good.
All ass and no class.
That Kournikova has been ranked as high as eight in the world, has played a Wimbledon semifinal, that her victims have included Capriati, Davenport, Hingis, Martinez, Seles, Sanchez-Vicario and Graf, was apparently not enough.
Not enough for the promo-people, that is, although it is good enough for some of the rest of us.
It might seem like harmless fun, but is the beauty-is-everything message really what the sport should be sending out to those legions of young tennis hopefuls it wants to attract? Methinks not.
Cricket promoters obviously missed their golden opportunity when they treated Imran Khan like just another player, even though the Pakistani legend is apparently a "stud-muffin," as one woman described him to me.
Hopefully, cricket and others will continue to miss those opportunities because there is no scarier sight in sport than that of the marketing division moving in to take over.
Injury has sent Kournikova sliding to 74 in world rankings, and it remains to be seen if she can win a tournament, let alone challenge the power of the Williams sisters or the finesse and determination of Hingis.
Is Kournikova a sideshow, or is centre court where she belongs?
Her presence has, of course, helped the event to gain extraordinary publicity. And it has given a tournament that sneaks into the $US140,000 ($336,000) fourth-tier category a taste of stardom.
Women's tennis seems to be enjoying the spotlight.
Kournikova has also drawn more people to the courts in Stanley St, which, in turn, is a reminder in the television age that tennis is a sport that can be much more enjoyable to watch in the flesh - whatever shape that flesh might be.
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