Austria Hungary makes demands that Serbia can accept. They're not starting a war without Germany's explicit backing.
Well, here's how I expect that to work out.
"What Serbia can accept" ends up being a promise by the Serbian government to investigate itself, with no outside oversight.
Since Serbian politicians are more than a bit worried by Apis, his regicide compatriots, and their Army clique, the investigation carefully leads nowhere.
Apis et al sponsor more destabilizing attacks on A-H. It's likely we'll even see a return of the guerilla bands that Serbia supported in various regions prior to A-H making her be more circumspect, in 1909.
At some point, A-H crumbles. Denied any effective response to violent acts perpetrated from sanctuaries in Serbia, and already in parlous condition, there can hardly be any other outcome.
A-H gets dismembered, with Russia ensuring the bits go to her clients.
And Germany is alone, helpless against whatever pressures the Franco-Russian Entente care to place on her. In the competitive atmosphere of the time, this won't be pretty.