"Exposure" is a tricky thing to pin down, and the technical term is "dose".
For one thing, there are many kinds of "radiation". Gamma radiation can penetrate right through you. Beta can't get as deep, but is more ionizing (and so is more likely to DNA damage). Thorium is an alpha emitter. Alpha radiation is the MOST ionizing form of radiation, but an alpha particle is so large, that outside of the body, it would be blocked by just a few feet of air, or at the worst, simply by your dead layer of skin.
The problem, is that an alpha emitter within the body puts it into a place that it WILL cause damage. Now, will that damage lead to cancer? That's a question I'm not prepared to answer.
For another, dose is time and concentration dependent.
Asbestos is dangerous in the lungs, because it stays there, without ever being bioabsorbed.
Iodine 131 has a relatively low level of radioactivity, but ingest even the smallest of doses of it, and the body will concentrate it into the thyroid, greatly increasing the chances of thyroid cancer.
When ingested, Thorium is most likely to pass directly through your body, but your lungs do not posses an anus. Either you cough it up, or more likely, it gets bioabsorbed. This is a double edged sword, because while it isn't allowed to linger in the lungs as long (which would increase the dose), it tends to end up being deposited into the skeleton (which is probably why thorium is known to cause blood cancers).