I'm aware that the Black Hand was a secret military group started by Serbian officers. That brings into question:
So there's a few things that to clear up first. Princip was a member of Young Bosnia a group that operated in today's Bosnia Herzegovina. This group although primarily consisting of Serbs also had Croatian and Bosnian Muslim members. Their over arching ideology was pan-slavism and freedom of south Slavs from Austro-Hungarian rule.
The Black Hand (Unification or Death) was a group based in Serbia consisting of some members of Serbian military / government. Their overarching ideology, although somewhat overlaping, was the unification of south -Slavs under the Serbian Karadjordjevic monarchy. But this group didn't have direct support or overt / official involvement from the Serbian government at the time.
So the Serbian government / monarchy wasnt involved in the planning or execution of the assassination plot in Sarajevo. But was willing (publically) cooperate to an extent with the AHE to placate the crisis. The rejection of the point of Austian delegates operating in Serbia was seen as a compromise of Serbian Sovereignty and thus unacceptable.
There is some disagreement among historians of the authenticity of Serbia's desire to accept AHE demands as much as possible but more accepted interpretation and view at the time boils down to:
The AHE had been having issues with unity in the empire because of so many competing ethnicities. And this problem was only getting worse with the rise of nationalism and internal issues in the empire.
Serbia was seen from the Austian perspective of fomenting discontent among the Empire's South Slav populations (Serbs, Croats, Slovenes and Bosnian Muslims) and elemets of the AHE government /military wanted war with Serbia.
Serbia was a newly formed nationalis Kingdom with expansionist ambitions mostly taking advantage of the decline of the Ottoman empire. The annexation of Bosnia by AHE and the Berlin peace conference where Serbia was forced to give up access to the Adriatic Sea (via Albania) stunted these ambitions.
AHE's internal issues with South Slavs and Serbia's external ambitions were bound to intersect at some point.
So the, then, and generally accept views are: AHE drafted the ultimatum to be rejected and lead to war and Serbia saw the stipulation as giving up Sovereignty and was left with no other option.
Some resources: The Balkans Misha Glenny The Serbs Tim Judah History of the Serbian People Vladimir Corovic (non english) Among others from my MA thesis that I can post later when I get home.