Of course the world figures he did it... Innocent people don't run.
Innocent people could indeed run:
i didnt' say it was a good choice but when there's a dead woman in your hotel room (regardless if you killed her or not) , and you've already been tried and convicted by the media for another woman's death, (even though she's technically just "missing") you're probably in a fight or flight mode, and maybe it looks like the least worst option at the time.
and if he had stayed in peru, maybe the local magistrate would have had him swinging from the gallows by sundown.
Even an innocent, with Van Der Sloot's notorious past, could envision not getting a fair trial because of said past and hence flee from Peru.