No health care experience (clinical, engineering, consulting, whatever), is a really good reason that you should go to a school with a health care concentration. If you don't have some kind of relevant experience, I think it would be tough to get your foot in the door at the other schools (depending on what you want to go into). Even at a school with a concentration, you will probably be a step behind if you are completely switching.
J&J is kind of a bad example to point to for recruiting, because they have a huge consumer products division, so their hiring base is more broad. Medtronic on the devices side is probably more representative. Though, if you look at the schools that J&J partners with (Wharton, Duke, Kellogg, I think maybe Haas), they all have health care specialties.
If you have some experience, you're probably alright at one of the top schools that specializes in what you want to do.