A strong immune system does tend to multiply the effectiveness of a vaccine though, not just add extra resistance on top of it, because vaccination works though the immune system.

A strong immune system is like having fit and healthy soldiers, while a vaccine is giving them experience and knowledge in fighting a particular enemy. Either one is better than neither, but if you've got both they build off each other.

You can see this in practice by comparing vaccinated and unvaccinated relative illness percentages in different age groups; vaccination reduces infection and illness in all age groups, but the efficacy is higher in younger people. Which seems unfair since they generally need it less, but that's just the way it works.