How are Kenward & Roger's degrees of freedom computed in PROC MIXED?

Question

I run the following SAS model:

PROC MIXED DATA=dat order=formatted ;
    CLASS LOT DOSE ;
    MODEL TITRELOG10 = DOSE  / s DDFM=KR ;
    RANDOM DOSE / subject=LOT type=UN ;
RUN; QUIT;

and it yields the following results: Now I run the same model except that I use a Toeplitz variance instead of an unstructured variance:

PROC MIXED DATA=dat order=formatted ;
    CLASS LOT DOSE ;
    MODEL TITRELOG10 = DOSE  / s DDFM=KR ;
    RANDOM DOSE / subject=LOT type=TOEPLITZ ;
RUN; QUIT;

it yields:

The behavior of the Kenward & Roger degrees of freedom sounds strange: with the unstructured matrix they are all equal, whereas this is not the case with the Toeplitz matrix. The results are exactly the same with the Satterthwaite degrees of freedom (moreover, isn't it strange too that Satterthwaite and K&R degrees of freedom are the same ?)

I don't master the degrees of freedom derivation and I am rather suspicious about the way they are derived in SAS, hence I would like to have your opinion about that.

EDIT: I precise that my data are balanced