How is the Eastern Orthodox Church turned inside out?

Okay, this has been bothering me for over a month now.

On May 25, the NYT’s Alessandra Stanley started a review of the TV show “Mental” with this lead:

*****

There is nothing wrong with turning a proven success inside out — reversible raincoats, “Grendel” and the Eastern Orthodox Church have all shown lasting appeal. Opposites aren’t always apposite, however: an Oreo cookie assembled backwards is a little too gooey to handle.

*****

For the life of me, I don’t know how or why the Eastern Orthodox Church is a proven success that’s been turned inside out.

I understand the proven success part. The Orthodox Church has been around a while.

But turned inside out? Like a reversible raincoat?

I asked a Greek Orthodox priest the other day and he had no idea.

Stanley is a former Rome correspondent for the Times who covered the Vatican extensively and wrote often about the Orthodox Church, as well. She knows what she means. But I don’t.

What does she mean?