Graph builder - confidence intervals for categorical variable

[#1]

When applying the Line Of Fit option in graph builder with a categorical variable on the x-axis you can calculate confidence intervals for each of the group means. If you choose unequal variance the confidence intervals are based on the individual group variances but how is the degrees of freedom for the t-distribution calculated? It appears to be based not on the individual sample sizes but the overall sample size. I wonder what is the theoretical rationale behind the calculation.  

[#2]

I will answer my own question:) It turns out that the confidence intervals given by JMP are too narrow. "Correct" confidence intervals can be calculated for example in SAS with the proc mixed procedure allowing a heterogeneous variance structure and specifying the degrees of freedom method as ddfm=KenwardRoger.