I'm increasingly of the opinion-- and I'm not alone-- that the better bet for highly capable students is to get out of undergraduate studies without debt, and not to worry over-much about the branding of one's diploma.
It depends on what they want to do afterwards. The brand does matter for finance and consulting jobs. It matters less for aspiring physicians and professors, I think, but for the latter group the graduate school matters a lot.
This is similar to my current opinion: graduate from a reasonable 4 year college (state uni, respectable-but-not-necessarily-top-tier private), and then a strong graduate program in your area of actual career interest/aspiration.
I'd even add, there's something to be said for backing it up one more step, and picking up a vocational certification on your way through high school, or during a gap year, so that you have the possibility of working your way through college with a job with a living wage, rather than at minimum wage.
