Your profs are right. I'm doing a double non-thesis (NUCL and AAE) at a tier-1 (or close at least) and we don't have a distinction between MS and ME. It's just a "non-thesis" MS. I'd just put MS on your resume and be prepared to explain your choice of non-thesis route.
Unless they're a national laboratory or a company big into egghead R&D (and most aren't) most employers are going to be fine with getting a MS who's not all wrapped up in the world of published research. MS research can sometimes be off-putting to a company that wants you to work on something different from your thesis topic.
My impression is that the thesis route is highly geared toward going for a PhD and teaching/research.
I'm not sure if writing a thesis is worse than the extra classwork (6 hours or so here) that you have to do, instead. Because I'm a masochist, I'm doing some research work as well, and it's lower-pressure than the advanced coursework. Then again, I don't have to formally defend it, which I imagine would be kind of nerve-wracking.