m-f dont think thats the case.
I've got a similar scenario on the go at the moment. This will be a non-fault claim if someone went into the back of the OP. There are a few ways to deal with this (as far as I'm aware)but the one thing you must do is inform your insurer of any incident, whether you intend to claim or not.
1. proceed with a claim through your own insurer, who will request you pay your excess and claim every cost back through 3rd party insurer. If this was the case your insurer would decide on the write off or not
2. claim direct through 3rd party yourself, having informed your insurer for info only. Basically this involves you claiming personally off the 3rd party for all damage. In this case the 3rd party would decide it was a write off or not, since they are footing the bill for repairs / replacement.
3. 3rd option is to use an accident management company to claim off the 3rd party (which is what we're attempting)
Options 2 and 3 are apparently only recommended if the 3rd party has admitted full liability for the incident.
I remain unconvinced that any insurer actually has your best interests at heart though after doing a bit of web research on the subject.