I am running a Fit Model where the effects are nested. The Means displayed in the Least Squares Means Table for the higher level effect (TT in my data), do not even come close to what a simple calculation of the means using Fit Y by X show.

The description of the Least Squares Means Table indicates that the Mean displayed is the "sample mean for the given level".

I would appreciate if someone more versed in Nested ANOVAs than I am can provide me with an explanation.
I have attached the data table with an embedded script.