Can a negative be proven?

"You Can Prove a Negative. It is widely believed that you can't prove a negative. Some people even think that it is a law of logic—you can't prove that Santa Claus, unicorns, the Loch Ness Monster, God, pink elephants, WMD in Iraq and Bigfoot don't exist. This widespread belief is flatly, 100% wrong."
- Source: Bloomsburg University of Pennsylvania here.

The Loch Ness Monster does not exist because it's claimed water home is a glacial lake only ten thousand years old.