IMO doing an extra year is not helpful to your CV unless you are otherwise an extremely poor applicant. Here's why:
1. publications are hard to get and it takes a long time to have a substantial high impact research project. This is generally something medical students cannot do because you will not get full credit (your principle investigator will). Also big research projects take a long time to complete and taking a year off is a big gamble. Reason being that you don't actually have a full year to get it done. Applications for residency are sent out in September and the "school year" finishes in May. So that's really only 4 months to do something if you take a year "off" after 4th year.
If you do it between 3rd and 4th year you'll have more time but again you may only get at most one publication and it likely won't be of any impact and you won't get full credit for it. Medical students typically jump on to ongoing projects and are not a significant contributor to the question being addressed, the design, analysis, or writing. Usually they just collect data, write a few paragraphs that are heavily edited and then get their name on the paper. But programs aren't dumb and when they ask about research, medical students often cannot adequately describe what was done or why.
Also, here's the thing, it takes a long time to design a project, get approval for the project from the IRB, get all the data for the project, analyze the data either on your own or with a statistician, write a paper, submit to journals, edit paper, and then get published. It will always take longer than you think. Always.
Plus, you can always get publications in residency because you'll have 2 years before fellowship applications to get a couple things done.
You also gotta think about what field you are applying for. If it isn't a competitive surgical field you likely don't need publications unless you are shooting for the top of the top tier. In any case, likely all you'll need is a few case reports, some poster presentations, and "research experience". But you must have strong board scores and grades. Case reports are easy and anyone can present one at some conference on a poster. But having an real research project that you are a significant part of is very difficult for a medical student.
2. degrees such as MPH and MBA are pretty useless. You can get a MBA after residency with night/weekend classes. A MPH is just useless in general if you are not doing public health and it will not strengthen your cv. Nor, will it help you in any field of medicine. All you get is a few extra letters on your white coat. I would challenge someone to explain how knowing epidemiology and epi research makes you better at performing surgery, stabilizing ICU patients, or treating sepsis.
I think the only useful one is PhD as that is something that very significantly strengthens your CV and is very important if you want to do research for part of your career.
So I highly disagree with taking a year off either after 4th year or between 3rd and 4th year. It is extremely difficult to significantly strengthen your CV if you haven't done anything up until that point and might be of minimal help depending on the field you are applying for. So I would not pick a medical school based on the ability to take an extra year to do nothing.