I don't know obviously what communication is between the replay booth but you definitely should want the replay booth to understand what the refs on the field think they called. And I think as a practical matter that does happen. I think I remember seeing a sound fx or something where, back when the ref was the reviewer, he would ask for detail from his guys what they thought they saw.
And that's good. You shouldn't apply some blind deference based on what you think a guy might have thought he saw. Take a catch, and the question is whether the guy got both feet in bounds. The guy takes three steps. The third step is out of bounds, just barely. So, the question is whether the ball was caught while the first step was still on the ground. The guy on the field calls it a catch.
You go to the replay booth, and it sees immediately that the third step was out of bounds. You would really like to know, in this case, what the ref thought he saw. If his call was based on a view that the ball was not caught yet on step 1, but that step 3 was in bounds, you want to know that. If the replay official sees that the third step was out of bounds, now you have a question of what deference to pay to the on field official. You shouldn't be inventing what you think he might have seen and apply discretion to something he didn't even call. If you said to him, "hey, we see on video the third step was out of bounds," and he would say, "oh really, I thought it was in bounds and that's why I made my call, but after that I'm not sure so call whatever you see on step 1," that's valuable information. And there is no way we should ever be giving deference -- particularly not near conclusive deference -- to things that were not seen or called by the on field ref. The first question from the replay booth should always be, "what do you have," and then deference should follow from that.