Italy offered surrender to the allies with certain terms under the Armistice of Cassibilie, most notably to help defend Italy against the inevitable German invasion which the Allies accepted

I am not sure you can really say the Allies made an exception on this point. You can read the short armistice here and there is no sign of a request from the Italians to "defend" Italy from the Germans.

Plans for occupation of Italy existed - after all the Germans had revised theirs already in July '43 just to be sure - and the issue had been considered during talks. But it was not included into the armistice that represented in fact an unconditional surrender; with the Italian representatives accepting the conditions dictated by the Allies and the Allies taking no obligation towards the Italian government.

The revised form of the long armistice would include (art. 18) a provision for the Allied forces occupation of Italian soil - but that would be in accordance to the Allies volition, and in no way subordinate to any Italian authority. The Italian forces were in fact required "to withdraw from these zones in accordance to the orders of the Supreme Commander of the Allied forces" and generally demanded to comply with any further demands the Allied would make, either of supplies, transportation, values; or in matters of public safety, laws and regulations, diplomatic relations. The extended armistice acknowledged at least on formal ground the full subordination of the Italian government to the Supreme Commander of the Allied forces and the United Nations.

With the war going on and civil war beginning in the North and Center regions of Italy, the relations between the Allies and the Italian Government became less one sided - as the allies seemed to appreciate the chance of establishing a friendly democratic government alredy during occupation and thus securing a safe transistion to the post war. Initiatives such as the creation of an Italian co-belligerant army, relations with the resistance movement, recognition from the Italian Communists of the government of national unity, helped re-establish some degree of authority to the Italian government, state and institutions. And the activity of the new generation of political leaders in those years would led eventually to milder terms in the peace treaty of 1947.

But in 1943 the armistice was - and was understood as such - an unconditional surrender.

Edit: sources - F. Catalano L'Italia dalla dittatura alla democrazia 1919-1948 ; G. Candeloro Storia dell'Italia moderna