Yes it is as you are being insured not the car. So you are being refused insurance because you own that car.
I can see where you're coming from, but UKjim is correct. It wouldn't count as being refused for insurance. It is merely an underwriter declining to cover a particular risk. The risk is being declined because it is not something the insurer covers, not the person being refused.
There are all manner of things insurers refuse to cover. Car types, postcode areas, driving history, occupations etc etc. None of those would count as an individual being refused cover, just an insurer declining a risk. Much like Saga only cover people over 50. Using your logic, everyone under 50 has had insurance refused by Saga?
Either way, it's a real shame if this does put the nail in the coffin of a lot of mk1 Jazz. They're getting thin on the ground as it is, without insurance problems.