I don't think it's "harder" in the sense of being at an enormous disadvantage because of the name of your school (although there may be some disadvantage). What *is* harder though is that you don't have all of the research-oriented resources in your back yard the way you would if you went to a highly research-oriented school. But there are ways around that; it just takes more initiative and planning on your part. So, let's say you do wind up at a non-research school. Here's what you do:
First, research fellowships for medical students are very plentiful. Pretty much every medical specialty organization offers them, as do various other institutions. So, during the summer between M1 and M2, you do an away research project at a research-oriented school and get funding via a med student research fellowship in that field. You have to apply for most of these programs in the late fall/early winter, so start looking for them sooner rather than later. In addition, obtaining one of these med student research fellowships has the added bonus of giving you an extra award to list on your CV.
Second, depending on how busy you are in med school, you may have some time during first year and/or second year to do some light clinical research on the side, like a case report or even a chart review. I wouldn't do anything though until after you take your first exam. If you do well on the exam and you feel like you had plenty of leftover free time, then you can approach some docs at your school and offer to write up a case report.
Third, pretty much any school in the country will allow you to take a fifth year to do research. Depending on the school, you may need to take a leave of absence, or they may have some other status for you while you're on your research year. But this is definitely something to ask about when you go on interviews. Just as there are summer research fellowships for med students, there are also year-long research fellowships for med students. These are highly competitive, and again, if you want to try for one, you need to prepare early. If you manage to get one, that will look *very* good on your CV.
Fourth, you have elective time during fourth year, at least some of which can probably be used for research. Again, this is something to ask about at interviews. Assuming that the school you attend would allow you to do a couple of elective months as a research away rotation, then you would have a similar scenario as you would for the summer between M1 and M2. In other words, you could try to get a second summer research-length fellowship. The actual timing of the research may not be exactly over the summer though, depending on your rotation and residency app schedule.
If you do all four of these things, your research credentials will be equal to if not better than many students who went to more research-oriented schools. You won't have the opportunities handed to you at a non-research school, but they're definitely available if you're willing to go out and get them. 🙂