Kind of, but not precisely correct.
The key to understanding influenza is understanding that the genome is in 8 pieces (“segmented”), so the big events are when those pieces get mixed in a new combination by two viruses infecting the same cell in the same host.
The thing that Paul can’t seem to grasp is that there are asymptomatic or mildly symptomatic infections all the time in all the different hosts.
Mutations are involved, of course, because the viral polymerase has an enormous error rate, but they are generally secondary.