It's a nonsense article. Pipes burst when they freeze, not when they thaw. They can't even get the basics right.
To be fair, and I say this after a couple of pints (and as someone who respects you)... they seem to be saying that the freezing water expands and puts stress on the joints. I believe they are saying that by leaving the tap in a drip state, whilst it will not prevent the tap/pipe from freezing, once the pipe thaws, it will allow the water to escape from the spout rather than a joint.
That said, if a joint has failed, when you turn the tap off, the leak will become obvious anyway.
