(Spoiler extended) What was Oberyn's alibi?

I was thinking a bit about the Purple Wedding, and about how Littlefinger's story doesn't fully make sense (why would Olenna even need to involve him and Sansa?).

I realized that everyone just sort of jumped to Tyrion as the only suspect, and yes he did look extremely suspicious.

But nobody thought that it was a bit shady that a Martell who has good reason to hate Baratheons and Lannisters and is probably the most notorious poisoner in the seven kingdoms was also at the wedding?

And then they even appoint him as a judge at the trial? Did he have some kind of airtight alibi that I just missed?