So I just had to give it a try using a simple curve to attempt to match the 'original' base image with a 'result from a stack'.
No 1 - This shows the 'Result from Balanced Stack' with its histogram and numbers.
No 2 - This shows my quick attempt to match the 'Original Base Image' with the 'Balanced Stack Result' using a curve. With histogram and numbers.
Whilst there are slight differences in the numbers and differences in the histogram to the eye they are pretty close. Another 10 minutes I suspect I could of got closer
And who forgot to save the images he adjusted