No official reason has been given for the decision, but the Herald understands that the Scottish Rugby Union did not want to be seen to be assisting the Kiwis, in the week that they face Scotland.
Whatever the reason, it's a shame.
Part of the reason the Kiwis ventured north for a few days was to promote the game and have a presence here, particularly as the match will be played in Workington, about 65 kilometres south of the Scottish border.
Having a training run - and signing autographs and posing for photos - in front of local schoolchildren and fans was a major cog in that strategy, which now won't be happening.
It would have been great exposure for the code, with television pictures and photos beamed across the country.
When asked for comment, a Kiwis spokesman said that "with only one training session prior to the Captain's run it will be a closed session".
Meanwhile, it's likely that several of the fringe squad players will get some game time on Saturday.
Coach David Kidwell is in a difficult situation. He knows the team has to win - and win well - against Scotland but also wants to reward some of the younger players for their efforts so far on tour.
Uncapped rookies like Te Maire Martin, David Fusitua, James Fisher-Harris and Joseph Tapine have been outstanding at training sessions, and impressed the coaching staff and management with their commitment on and off the field.
A total of five players have yet to feature on tour so far; the quartet named above as well as one test Kiwi Dallin Watene-Zelezniak.
Kidwell needs to manage the tradeoff between retaining some combinations and experience, and giving some of the younger players a chance to shine.
However, throwing rookies in at Kiwis level is no longer the risk it was in the 1980s or 1990s, when players were plucked straight from club football in Auckland, Wellington or Christchurch.
Now everyone in the New Zealand squad has already made their name in the NRL, and have plenty of big match experience.
The injured duo of Jason Nightingale (ankle) and Jared Waerea-Hargreaves (knee) are also likely to be eligible for selection this week.
The Kiwis travel to Carlisle on Wednesday (Thursday NZT). They'll be based in the Cumbrian city for the week, only travelling to Workington for the captain's run and test match.
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