Rhythmdvl, sorry for taking so long to get back to you.
I haven’t really thought about the grammar of this before. FWIW, I think it’s a matter of whether or not it makes sense to think of the object in question as a representative of one thing or class of things, or rather as one of many types of something. To draw some parallels with other geological terms:
- A mineral or rock name is usually reserved for a material with specific characteristics. For minerals, those characteristics include chemical formula, crystalline structure, density, hardness, color, luster, cleavage and fracture. For rocks there’s a bit more slop, but they are typically defined by the presence of particular minerals and textures (different criteria exist for igneous, sedimentary and metamorphic rocks). Sometimes these names are also used for a class of similar minerals or rocks as an all-purpose moniker (e.g., mica as a general name for a sheet-like, platy mineral, or sandstone as a general name for all rocks that are composed of siliciclastic grains of a certain size range).
For either of these circumstances we’d refer to the material in question the same way you’d talk about sugar: “some mica,” “some sandstone.”
- If we wanted to acknowledge that there were different types within a given class, we’d take that all-purpose moniker and make it a plural noun. We could also then discuss a generic example of that plural noun.
Just as a biologist might now talk about various “sugars,” and point to glucose as an example of “a sugar,” geologists can now talk about various “micas” or “sandstones” and point to muscovite and arkose as examples of “a mica” and “a sandstone,” respectively.
So to me, the term meteorite falls under the second example above, because it is an all-purpose moniker that describes a particular class of rocks (those that are extraterrestrial in origin), and because there are several possible types (e.g., carbonaceous chondrite is an example of “a meteorite”).
None of this stops you, of course, from referring to “a fragment of meteorite” or “some meteoritic material.” It would be clear to any geologist exactly what you meant, and I don’t think any would want to argue with you about the grammar. Just because we do something out of custom doesn’t mean it’s linguistically correct. 
SilentKnight, it’s really hard to say what the rock might be without seeing it in person. (Look at how much yakking there was about what kind of rocks the martian Pathfinder was seeing!) If there is any way you can post a picture of it, I’d be willing to hazard a guess. If not, and you’re really itching to know, drop me an email & I’ll give you my address so that you can send me a small piece. Knowing exactly where it was found will also help narrow down the possibilities for a source.
BTW, not to be too alarmist or anything, but if there’s a chance that this IS a piece of industrial slag, you might want to be careful about handling it with your bare hands for too long (at least wash up with lots of soap afterward).