Why is the minimum voltage not -Vcc?
Vcesat is BY DEFINITION the lowest voltage that a fully turned on CE junction can assume. You CANNOT get a lower Vce voltage BECAUSE you have defined this as the lowest voltage possible. That is what sat (= saturated) means. = turned as on as it is able to be in this context. 

You can pull the Collector lower by some external or independent means, but that's irrelevant here. Here the mechanism of lowering Vout is by reducing Vce - and you have defined how low that can be by defining a value called Vcesat.

So

Your answer "Vcc- + Vcesat" translates to   


"The lowest negative voltage available   


PLUS   


The smallest possible Vce value in this situation". 


If you can get lower then 2 x Lowest-possible values then something is wrong.