Actually, no, it turns out to be false.

According to Snopes and the "onions become more toxic than spoiled mayo" e-mails:
snopes.com: Cut Onions Contamination

And also one of the myth's posted on "onions-usa"
The National Onion Association

Also on hoax or fact it has the exact story about the farmer and it's false
Left over, Cut onions become toxic - Facts Analysis | Health

It says onions create sulfuric acid. Crazy! But bacteria may like moisture but not acid. I think we're safe after all. The onions-usa says we can store them safely contained for up to 7 days after cutting in the refridgerator.