That's actually quite different from what I've discovered. As you might know, I've been exploring both Orthodoxy and Catholicism, but more of Catholicism recently.
What Rome requires the Eastern Catholics to assent to is that their approach is valid and true. That is, the immaculate conception, original sin, categorization of sins, etc is all true. They also have come to the agreement that the Eastern approach is also very true, that is the lack of original sin, immaculate conception, filioque, etc. That is, they assent that each others' teachings or approaches are valid and true.
Finally, and most importantly, the Eastern Catholics recognize Rome's bishop as the pope. There is no equivalent in Orthodoxy.
Catholics assert that the schism is a disagreement over church politics. Orthodoxy asserts that it is a disagreement over theology. I assert that it is mostly a disagreement over church politics by far and also a disagreement on some very important theological issues, papal infallibility being one of them (and now this annulment thing).
The Roman Catholics have treated Eastern Orthodox Christians with a lot of crap throughout history, and I feel the pain of this too, trust me.
The point that I would like to make is that Roman Catholics must acknowledge that the Eastern approach is equally valid as the Roman approach to theology, and for the most part is not a "submission" except for a few things that I already mentioned.