I would be interested to know how you get on there! I suspect they will take the vets side as they are a vet organisation.
A few years ago - my old vet gave my dog a massive steroid injection and she then got diabetes. Had I known about the risk I would never had let him give it her. I wanted to complain, so wrote to the cheif vet and then heard nothing else.
The mistake my vet made was to prescribe a drug with wrong advice on administration to my dog,and without prior blood tests as recommended by drug manufactors this drug should not have been given to dogs over six years of age mine was ,also a week later after being told my dog had no problems and a and full examination he died of a enlarged spleen which caused a massive internal bleed which they admit they missed and should of picked up