The problem with this is that if there's a fix then you have to be reasonable and allow them to give it a go.
Maybe.
In law, it comes down to whether a Court decides you have accepted the goods. If you reject at the first reasonable opportunity after noticing the fault, and the fault is sufficiently serious as to render the goods substantially unfit for purpose, then you can refuse a repair and insist on a refund.
If you have kept using the goods after noticing the fault, and certainly if you have kept using them after noticing the fault, then you will likely be deemed to have accepted them, and the dealer then only has to offer a repair (unless repair is not possible).
To be able to reject when repair is possible, if you can answer 'Yes' to the two questions:
1. Am I rejecting the goods at the first possible opportunity?
2. Is the fault sufficiently serious as to render the goods substantially unfit for purpose?
then you have a reasonable chance in law of winning your case if the dealer refuses to refund and it goes to Court.
Some cases are clear cut. For example, if you're driving home after collecting the car and a conrod goes through the side of the crankcase, or the layshaft breaks and the gearbox seizes solid, then you can reject the car out of hand; you don't have to accept an offer of a replacement engine or gearbox. These sort of things thankfully happen only very rarely.
With this issue, I'd say it's less clear, since the car can still be driven in most circumstances - you can't insist on a refund just because something isn't very good. It would need a test case to decide for sure, and personally I wouldn't want to chance it; you could be out of pocket for more than the value of the car if you lose, and still end up having to accept a repair.
It would all come down to whether a County Court Judge decided the fault was sufficiently serious as to render the car substantially unfit for purpose. In practice, the Court would rely on the opinion of independent witnesses; I'm sure the dealer would offer a robust defence, so you'd need to have your own independent expert statement that the car was, on balance of probability, substantially defective at the time of original sale.
Arguing this in Court would likely cost the loser tens of thousands of pounds and in view of the high profile of this now, Fiat might throw a lot of muscle at this. Before rejecting, you'd certainly have to ask yourself "Do I feel lucky?".
