The Eastern Orthodox leaders stood on the sidelines with the other religious leaders in attendance... like the muslims, Buddists, Hindus and others.
They paid their respects but did participate in the service.
There were a couple of threads with pictures about this subject after the funeral.
>> I think those priests you saw were the eastern version of the Roman Catholic Church. <<
Unless Fox and CNN screwed up gravely.
CNN: (from memory) "Coming up: Something that has not been witnessed in almost fourteen hundred years. [Later:] This is truly a monumental event in the history of Christianity. What is about to be read is the prayer of the patriarchs. Every patriarch of the ancient church -- not just the Roman church -- is gathered here for the first time in 1400 years. Copt, Russian, Greek."
What followed was the Patriarchs forming a half-circle around the casket and praying in Greek. They had very varied clothing, including headwear that varied from what looked like a classical fantasy-realm crown, to elaborate, ornate and exotic tiaras.