Brahman is the only thing which is unmixed with MAyA. What is referred to as the substratum of the entire universe is Brahman; the same thing when referred to as the substratum of the jIva is called Atman.
Brahman which is the same as Atman is the only thing which is untouched by MAyA. Hence it is called ‘shuddha brahman’ – that is why the shloka has ‘shuddha Brahmani’. Even a little mixture of MAyA will make it different. Ishvara Himself has such a mixture of MAyA.
The universe which is totally mixed with that MAyA is being administered by that Ishvara, who has MAyA with him (*MAyA-sahita Ishvarah). Brahman does not do any such thing as administration of the universe. Brahman has nothing to do with the universe or its affairs.
Of course it is the substratum, basis of the universe; but from that Brahman it was MAyA that produced the vision of the universe. Brahman is not related to the universe. The dim light produces the vision of the snake from the rope, but the rope in reality has no relationship with the snake. It is an unmixed rope all the time.
That kind of unmixed thing-in-itself is what is called shuddha Brahman. Instead of the saguna form of Ishvara, if the mind is focussed on nirguna Brahman, that is said to be ‘samAdhAnaM’.