He hates the Lannisters. In the premiere, Oberyn makes it very clear to Tyrion that he has reasons to seek revenge against the Lannisters: Tywin's bannerman The Mountain raped and killed Oberyn's sister, Elia, before murdering her children.
Within hours of his arrival at King's Landing, Oberyn shows he isn't afraid to get violent, stabbing his dagger through a man's wrist for singing the Lannisters' song at the brothel.
Why it couldn't be him:
Oberyn gets into a passive-aggressive argument with Tywin and Cersei Lannister at the wedding, but he doesn't approach the head table or have any direct interaction with Joffrey.
The latest:
Tywin confronts Oberyn in the brothel about having studied poisons, a pretty strong case against him. Though Tywin makes a power play by involving Oberyn in Tyrion's jury, Oberyn could still be a suspect.