Applied math/statistics can be a great premed major for those who have any sort of quantitative bent. It hits the sweet spot of enhancing employment prospects, but with less grade-deflation exposure than CS or engineering. Research settings - medical or otherwise - will always need and value people with a strong stats skillset, so acquiring that skillset is likely to pay off whether the student ends up in med school or not. Public health can indeed be a great focus that can both prepare one for med school and offer alternatives; but a stats background is especially desirable in that field, even more so than in medicine, because it all hinges on population-level data analysis.