Without getting into too many details, the misunderstanding happened because of an equivocation of the concept עצמותו ומהותו. Outside of Chabad the term means God Himself, i.e. His essence, and that is how the term was always understood, by the Jewish philosophers. Thus when, for instance, the Rambam wrote God is unknowable in essence rather all that we can know is his existence, he meant that all we can know is ידיעת מציאתו ולא מהותו. [In regards to what the Rambam calls God שכל פשוט, he does mean a mind like ours, as he clearly states in direct opposition to Aristotle].
It is precisely this point that the Maharal takes up with the Rambam, God is unknown in every sense and way and cannot be spoken of at all. A consequence of this was that even in Gods’ interactions with his creations is a secondary manner (I am not referring to השגחה, rather to the knowledge of Him). For instance according the Rambam we can know God negatively, i.e. via negitiva, but according to the Maharal we can’t). Following in his footsteps it became common practice not to speak about God Himself in a direct way, meaning all we can know is a roundabout way, סובב, that God, so to speak, ‘takes care of the world’, however anything pertaining to God not as He interacts with the world, ממלא כל עלמין, we can have absolutely no knowledge about. The ramifications of this approach in a simplified manner is that our ‘job’ in this world, which is only what we can have a שייכות to is strictly the letter of the law.
Chassidus in general, and Chabad in particular, reformulated the concept of our knowledge of God. Without getting into details, Chassidus teaches that knowledge of סובב is actually a higher form than of ממלא and that a human being can achieve even this level. Chassidus further teaches that there is a difference between אור אין סוף and אין סוף itself. In other words, even as it relates to this world there are many ‘levels’ of Divine manifestations as it pertains to us. How it is manifested and it’s relationship with the physical is a lengthy discussion which we will not get into now, however what is patently clear according to this is that everything, including the physical is אלקות; and everything even רוחניות was created and is not God in the strict sense.
Now, what Chassidus and the Litvishe (for lack of better word) understanding of the Divine Hierarchy have in common is that they do not speak about God himself. However what the God that is unknowable is a dispute as mentioned above. For according the Litveshe understanding Kabbalah through speaking of the Divine Attributes ספירות is in itself a discussion of God that we cannot understand, ממלא; but, according to Chassidus, this is סובב and can be grasped through contemplation דעתא עילאה (at least by the ‘higher souls’). עצו”ה according to the litvishe is God himself, according to Chassidus we never discuss God himself, rather these are all forms of emanation that pertains to us.
To sum it up. No one believes that we can speak of, let alone grasp, God Himself. The issue at hand is rather what is the Zoher speaking of, God Himself or rather סובב. Therefore there is always an equivicotion between the terms used in Chassidus and the Litvishe, and do not mean the same thing. When the Lubabitcher Rebbe said that a Rebbe is עצו”ה he did not mean God HImself as a Litvishe would understand it.