Nope, this does not have to be true. There are plenty of schools that take research very seriously and understand that good science isn't done in a short little block. I have visited several schools - Yale, UPenn, University of Michigan, Pitt - where a good number of students I met were involved in research year-round. Certainly, it's a tough balance and students have to prioritize based on their current workload, but there culture of research is definitely there. At Yale, for example, I visited a coffee shop after my interview day and overheard several medical students chatting with other students or with their PI's about the research they were about to go and do during the afternoon. At least at the schools I have mentioned, my faculty interviewers have assured me that more than just a few students find time to be seriously involved in research and more than just a few students choose to pursue research during their MS1, MS2, and MS4 years. I've also asked this question of all my student interviewers and 3/4 times the student interviewing me was actively involved in research and has been since MS1.
I think that a critical component in a medical school that accommodates research is flexibility. At Michigan, you choose when you take your weekly quizzes. At UPenn, tests only come every few weeks so you can schedule research around studying over a longer period. Those are just some examples. I don't know as much about this program since I don't have an interview there, but graduates of the Harvard HST program have told me that plenty of students participate in research year-round there as well.
Bottom line: I think it does matter where you go to school for research. You want a school that has money for your research and money to fund you. You want to go to a school where the PIs are well funded and thus happy to take time to mentor students, even medical students. Plus, if you have a good idea about what you want to research, you certainly want to end up at a school that has a strong host of PIs who study the thing you are interested in.
Edit: When I ask about research, I specifically don't ask about the experiences of students who take extra time through a special program to do research. I am interested in the straightforward 4 year MD
Edit2: OP, I now realize that we both interviewed at Pitt and at Michigan...so I guess we just got very different students/faculty by chance.