My situation was a bit different, but I was a finance major that also took all the pre-reqs while in U-grad. Then, 12 years later, I took a bunch of mid-upper level science courses prior to applying. I did not retake any of the pre-req's though.
That being said, I'm VERY glad that I took all of those science courses (above and beyond the basic pre-reqs), which was necessary to reestablish an academic track record for applying etc. Again, my timeline was not traditional, but I feel those courses (physio, biochem, micro, immuno) have, and will in second year, come in handy in a pretty big way.
Also, during our welcome ceromony, it was very clear that the vast majority (though having non-science could help you stand out in lieu of this) of my peers were science majors and came into med school with some very strong backgrounds. Many have had a full year in biochem. And biochem is a lot of memorization of pathways and enzymes (as most of you well know..lol). So, the more you've been exposed (and have had to memorize in the past), the better off you'll be. Don't underestimate this benefit. It was MUCH easier to memorize glycolysis, tca, and the ETC processes having had that stuff before. So, keep that in mind. It's a big help.
So, NO, you don't need to be a science major. Others have said that it could be of strategic advantage to go another route (provided you enjoy whatever major you choose). But, try to take as many science electives as possible. Focus on physio, cell bio, biochem, micro, and immuno. Also, if you can take a cadaver based anatomy course, that would be great. Ofcourse all these classess are not necessary, but try to get in some of them.