It'll be interesting to hear the outcome of what the garage says. They could well have been duped themselves, however, they must make every effort to ensure a car is legit and clearly as others have already said and as is laid down in law, a car that has previously been written off and repaired, the fact must be made known to the buyer prior to parting with any money.
The problem is that cars are only recorded by HPI as 'written off' if an insurance company informs them that a claim has been settled on a total loss basis.
If the car was damaged but sold on as unrecorded salvage, then another garage could repair the car and sell it on without any legal obligation to disclose what they had done. The car's HPI record will be clear and there is no way that someone subsequently purchasing the car would ever know.
Google 'unrecorded salvage' and you'll find hundreds, if not thousands, of damaged cars for sale. A few will be broken for parts, but most will be bought, repaired and sold on without the buyer being any the wiser.
The law doesn't distinguish between an unrecorded car sold with a split bumper and an unrecorded car sold with major accident damage.
It's a massive loophole. AIUI, the only recourse a subsequent buyer has in this situation is if the repairs were not done to at least a roadworthy standard, or if they were so badly done that the car is not fit for purpose.
Ellie's car was sold with a clear HPI certificate from the selling dealer. There's no reason to suppose the certificate isn't genuine, so either there has been a major failure in the system (in which case the selling dealer may be able to claim compensation from HPI), or the car was never declared a total loss by an insurance company.
So the big question I have now is how do Fiat know it was damaged beyond economic repair, if it has never been declared a total loss?
I could speculate about what might have happened (and it won't be long before someone else does exactly that), but Ellie needs hard facts to take this forward. She is the loser right now, and it certainy isn't her fault.
Ellie, the HPI certificate shows the car as only having one registered former keeper. I'd suggest you put as much effort as you can into finding out who that former keeper was. I'm sure they have a story to tell.