I'll separate your question into a few parts.

First, organic (carbon containing) materials can be quite toxic. For example, methanol (so-called "wood alcohol" because it once was chiefly produced by distillation of wood degradation products. See, for example: http://www.bartleby.com/65/me/methanol2.html) is well known to be highly poisonous, causing blindness and death upon ingestion (drinking it). In Salt Lake City (near where I live), a university teacher brought methanol from his research lab to a youth center he volunteered at. His mistake was transporting it in a vodka bottle. It was given to a custodian to use as a cleaning solvent. The custodian kept it locked in a storage locker, but somehow,one of the kids at the youth center got into the locker and brought the bottle to a party, thinking it was vodka. Because methanol looks and smells like ethanol (the alcohol found in alcoholic beverages), the kids mixed it with alcohol and drank it. I recall at least one died of methanol poisoning, perhaps two.

Second, to produce moonshine (ethanol), you mix grains with water and yeast to ferment the grains into an alcoholic liquid. If you were making beer, you'd put it in a bottle at this point and be done. When making moonshine, you perform a distillation. This involves heating the liquid, so that the more volatile components boil off--for example, the alcohols are more volatile than water (they boil at a lower temperature). The boiling pot is connected to a condenser, so that all the vapors are forced through the condenser. The condenser is a cooler, so that the vapors turn into a liquid again and drip out. You throw away the stuff that comes out before the alcohol comes out, and when all the alcohol is condensed, you'd be done. You know when the alcohol is done distilling because the temperature of the pot is hotter than the boiling point of the alcohol (you've heated beyond the boiling point, so it has all boiled off). Third, it turns out that old auto radiators make great condensers. However, auto radiators have lots of lead based solders that are used in them. As a result, lead is extracted and ends up in the moonshine, leading to high incidences of lead poisoning in the moonshine belt (WVa, KY, TN, etc). See, for example: http://www.cdc.gov/mmwr/preview/mmwrhtml/00016616.htm or http://www.public-health.uiowa.edu/fuortes/met_lead.doc

Lastly, it is much more expensive to buy grains than to buy methanol. It was common (may still be) for moonshiners to increase their profit by diluting their product with methanol. Methanol is readily available as a cleaning solvent. There is only so much water that can be added before moonshine will taste dilute. Adding methanol probably maintains the "alcoholic" taste, and decreases the cost of their product. When too much is used, cases of poisoning are noticed.

I hope that answers your question. The take home message is that moonshine poisoning is a result of careless production or greed (or in some cases just overindulgence).

Regards,
Mike