Roger Pearse

The Wikipedia article rather suggests that matters may be more complex, tho.

judge

Yes, they are not in official communion with Rome although there has been dialogue.
They certainly dont agree that mary is the mother of god, or with Theotokos which was the issue at Epessus, so I think if we say they recognise Ephesus it is a little misleading.
I think we need to be careful of taking the RCC slant on these things.
The Roman Catholic Church actually believes they are the true church and that Jesus gave Peter the keys to the kingdom.
It colours their reporting of these things IMHO.

They invent the so called "schism" of 431 CE, painting themselves as the true church. In their world as they are the true church, the correct situation has been for any other church to be "correct" they should admit in some way that the RCC is the correct church as well, and has proper authority.
Protestants of course go along with this stuff as they see themselves reforming the true church.
In the end it is just a way of controlling people by telling them you must come through us to come to the Divine .