That's not exactly true. Some schools say they want your requirements done when you matriculate, but there are schools (eg Weill Cornell) that say they want them done by January of the year in which you plan to matriculate - basically by the start of your last semester in college if you go straight to med school after senior year.
So there are some schools where you may not qualify if you don't have or are not taking your reqs by the time you are interviewing. However, in my personal experience, some of those schools are willing to grant waivers if you can prove that you will definitely get the courses done by the time you matriculate by showing them the classes you are currently taking or are enrolled in. You should check the requirements pages of the schools you are interested in and contact their admissions office if necessary.