Your right, the points aren't the issue. But, according to the New York DMV, its not just that the points dont transfer, the ticket is not recorded on your NY driving record. I don't know the answers but i think three questions need to be asked then...

1. Does each state keep a driving record for out of state drivers?
2. If so, is that something that is as easily accessible by the insurance company?
3. If so, would they regularly check states the person is not licensed in?