Interesting. This is not the case in my Antiochian Orthodox parish. My wife and I were married in an Episcopal Church, but there was no inquiry where we were married or even if it was a church ceremony.
I have not seen any "remarriage" ceremonies in the parish. Maybe that's because we are 95% converts (not counting the children).
Now that's interesting. We have a substantial number of converts from Protestantism and they all have been remarried in the Church. As recently as 20 years ago, the GOA required it for Catholics too. We have some converts from Episcopalianism. I'll ask them Sunday what they did. Bottom line is that I suspect each jurisdiction has its own rules on this question.