
Hope I've got.this right .
It sounds like your insurance had not started when he had the vaccine .
Then the vet told.u his later illness although close in time was not connected with the vaccine?
By this time u had an insurance. If that's correct I would.start with the vet and get copies of.their records incase they have incorrectly filled in the form . I would also speak to the vet and remind them of what they said and see why has been written down .hopefully that will give some clarity. If the vet has made an error his records and an explanation by them should help with challenging the claim .
If u arnt happy after that put in a complaint to the insurance and then if that doesn't sort everything to your satisfaction you can go to the ombudsman .
Sounds to me that dates maybe the issue
As for.the vaccine there are risks with any vaccine that have to be weighed up before vaccinating .convention will say the risk of pneumonia or other serious ill health is less.than risk of.getting the disease. Its for.the owner and vet to decide which risk we take. Have a read of some other vaccination threads for.the future.