As a Mormon, I can tell you that it’s a totally plausible story; nearly everyone I’ve asked (who was old enough at the time) has said something similar.
The comments here show a lack of understanding about how Mormons work, which isn’t too surprising since we’re a small group, so I’m not blaming anyone, but yeah, it’s completely plausible and in line with a faithful Mormon’s reaction.
The idea was that the LDS Church needed a revelation from God to change the policy (the beginnings of which are unclear and lost in the mists of time; Joseph Smith did ordain black men to the priesthood, and it changed sometime later, no one really knows exactly when or why–there’s no scripture). It’s on record that some of the presidents of the LDS Church had wanted to change it since at least the 50’s, and were unhappy that the change couldn’t be made yet. The leadership of the church asked all members to pray for the change. So it was widely talked about as a hoped-for possibility.
The announcement did, in fact, come as a sudden change, not as a process. Once it was felt that the time was right, it was announced by the prophet, and that was it.
I’ve asked a lot of people what it was like, and the answers I’ve gotten have been universally that it was a big, emotional deal. One guy’s father had served as a mission president somewhere I don’t recall (but with a large black population), and he called up Salt Lake and begged to be sent back. (Mission presidents are called for a term of 3 years.) Some older people grumbled, and they left–the feeling was good riddance.
I was 4 at the time, so I don’t remember it myself.
Mormons are used to the idea that things can change, and that God has better things in store for us when we’re ready. We hope for a lot of things that haven’t happened yet, and that’s in line with Church doctrine, not in opposition to it. Here is the 9th Article of Faith: " We believe all that God has revealed, all that He does now reveal, and we believe that He will yet reveal many great and important things pertaining to the Kingdom of God."
Now whether Romney was driving home from law school or not, I don’t know. But I’m willing to believe that he was driving home from somewhere and had that reaction.