I'm not an EMT and never thought of being one.
We have several former EMTs in our class as well as various other health people, including former nurses, PTs, etc. I don't think anyone's going to give you a hard time, but I don't think anyone's going to necessarily think of you highly or be green with envy over the fact that you have "additional" training. What I've been told by nurses, EMTs, and other health people who have gone through med school is that you may have a technical advantage -- meaning starting IVs, intubating, knowing what an NG or ET tube is -- but you may find yourself stuck in the way an EMT thinks. Arguably an EMT and nurse don't evaluate patients in the same way (ever read a nurse's note? An EMT note?), and along a similar vein, an MD and EMT don't evaluate patients in the same way.
What the person who told you that other med students may look down on you was referring to, and this is simply my opinion, is the holier-than-thou attitude some med students take with regard to the allied health professionals and the non-MD practitioners. As a med student you will UNDOUBTEDLY hear snide remarks about nurses, EMTs, chiropractors, and if you're at an allopathic school, probably of osteopathic med students as well. What you should understand is that these comments are born out of frustrating contact with one of these types of people or just plain ignorance. If you hear it as a first-year, I'd opt for the latter as the reason why your fellow MS1s are bad-mouthing them.
If you're an EMT, this will be your chance to educate a new group of would-be doctors on what EMTs do and why they're important. We med students no such education and our only interaction with them is usually in the EM clerkship/rotation.