Well, they didn't exactly say it wasn't possible. Only that it would be difficult and undesirable. So of course, I had to prove them wrong. And here's my proof.
It is entirely possible to tat with 100% wool yarn!
I find the results of this little experiment quite pleasing. One of the key factors in felting wool is agitation. Now making all those little knots causes a bit of agitation on it's own, and so the yarn becomes ever so slightly felted while working with it. That, coupled with the fuzziness of the wool, means that stitch definition is somewhat lost. However, rather than seeing this as a negative occurrence, I rather like it. Now, instead of seeing all that texture and individual rings and chains, the eye sees rather a solid (well, not solid, as it's lace, but you get my point) piece of fabric.
For anyone who is considering trying this themselves, I've used 100% wool laceweight yarn. And yes, it's shuttle tatted. The biggest key in working with this yarn was tension. Working with regular tatting thread (which is more of a cord, really) you get used to being able to pull your tension very tightly. Yarn is so much loftier than thread (or cord), so pulling your tension too tightly makes it very difficult to close rings. Not to mention it puts even more stress and agitation on the yarn, which will cause more felting.
So there, more proof that you really can tat with anything even resembling thread! Now I'm thinking up all sorts of other oddball materials that could be tatted with...