Prism fits a mixed effects model. It treats the main factor (that defines the data set columns) as a fixed factor, and the nested factor as a random factor. Review the difference.  

If there are no missing values, this analysis gives identical results to a simple t test or one-way ANOVA where only the mean of each subcolumn is presented to the analysis. When there are missing values, there is no shortcut.

If your statistical consultants want to know exactly how Prism computes a nested t test, show them this faq which gives an example in Prism along with corresponding R and SAS code.