Dialogue in ST V suggests that it was a new ship. There is nothing on-screen to suggest otherwise. What Roddenberry said doesn't matter because he had nothing to do with the production of the movies at this point and just liked to make statements like that so nobody would forget he was there.
It doesn't seem all that mysterious. A ship was being built when the 1701 was scuttled. After the destruction of the 1701 it was descided to name the new ship "Enterprise." While ship names are often chosen even before construction is started, it is not uncommon for names to be changed before actual commissioning. In fact, the descision to name her Enterprise may have come at the same time Star Fleet decided to decommission the 1701 before Kirk stole her.
"Canon is only important to certain people because they have to cling to their knowledge of the minutiae. Open your mind! Be a Star Trek fan and open your mind and say, 'Where does Star Trek want to take me now'." - Leonard Nimoy