Disclaimer: I'm a 4th year, currently applying in radiology. I might not know anything. I might actually be a dog. You should get advice from a good mentor in person, not from a message board.
First, radiologists who are currently practicing didn't match in the current competitive environment; it's really a different environment for the past couple of years as opposed to even five or six years ago. (I don't have the statistics to back this up on hand; perhaps someone else could post a link to them?)
Second, my impression of this process is that KerleyB is absolutely right. A graduate of a US allopathic school who has above average board scores and decent clinical grades and who is able to communicate a sincere interest in radiology will certainly be able to match
somewhere. (As long as s/he applies broadly and doesn't come across as a complete whack job at his/her interviews.)
Third, research can really strengthen an application. If you have some hole in your application (so-so board scores, mediocre clinical grades, some other weird thing), you can
partially compensate with research. It's just one more way for you to convince programs that they want you. Or, if you want to shoot for more academic centers or you want to have a better chance at matching in a particular city, research is an important way to make yourself more attractive.
Fourth, the term "research" covers a multitide of activities. Most academic radiology departments have a bunch of projects which would qualify as research (and lead to publications or presentations, the key tangible of the process). These projects might be: bench research, statistical analysis, generating graphs, preparing an educational poster, writing up a case report, organizing teaching files. There are lots of possibilities, depending on your inclination. You can probably find something that appeals to you that won't feel too much like making license plates.
Fifth, if you start research at the end of your first year, you can build up both a project and a mentor-protege relationship over the next two-and-a-half years. Both can be important assets in the application process, which starts sooner than most medical students think. If you start early, you can definitely turn that to your advantage.
To sum up, it's not actually
required, but your dean is right; research helps. If you want to do everything you can to advance your career, you'll find a project.
BTW (1), if you're thinking about this kind of stuff now, you could get a lot out of reading
Iserson's Getting Into a Residency. It's pretty readable, and it spells things out for you pretty clearly. And again, you can get a big advantage out of reading it at the end of your first year, rather than at the end of your third.
BTW (2), if you change your mind about radiology, a serious commitment to any of the kinds of research will definitely help you in almost any specialty you might apply to. Obviously, if you were applying to surgery, surgery-related surgery is best, but it matters less than you think. If you can demonstrate an ability to focus on something and some of the basic research skills (organized thinking, statistics, writing, etc.), you'll really help yourself in any field.