I do not think that the importance result is based on k. The help system says:
Factor values are constructed from observed combinations
using a k-nearest neighbors approach, in order to account for correlation. This option
treats observed variance and covariance as representative of the covariance structure for
your factors. Use this option when you believe that your factors are correlated. Note that
this option is sensitive to the number of rows in the data table. If used with a small number
of rows, the results can be unreliable.
Further:
Note: Variable importance indices are constructed using Monte Carlo sampling. For this reason, you can expect some variation in importance index values from one run to another.
In other words, a k-nearest neighbors approach is used to cluster observations so that the covariance structure of the data can be maintained. These observations are put into the model to get predicted values. Now, repeat (this is the Monte Carlo part) by choosing a new set of observations. See how much a change in a single factor made so that you can assess the importance of that variable.
I do not know all of the details of the k-nearest neighbors approach that is used, but I would guess that if a choice of k is made, it would be the one that describes the data the best. Look at the k-nearest neighbors clustering technique in the help section to see how JMP "optimally" chooses a k in that situation. If this approach is truly followed, I do not know what range of k is explored. Either way, I would bet that a range of k values are used due to the monte carlo simulation that is going on.
Dan Obermiller