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Why does JMP use the F-distribution, not T-distribution, as the basis of Power calculations?

JMP notes that the F distribution is used as the basis of the calculations for the one sample and two sample means tests in this document.

But I had previously assumed that JMP would make its power calcs using the T-distribution since the T distribution is basis of the one and two-sample tests typically.  Nevertheless, I would expect power calculations to give the same answer either way (using F or T appropriately).  But I can't seem to obtain the same results as JMP when I use a T-distribution for my own power calcs. 

So my questions are: (1) Why does JMP use the F statistic and F-distribution for power calcs?   (2) In theory, should it result in the same answer as doing power calculations using a t statistic and T distribution?

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