There's often a big controversy over whether atheists or theists have the burden of proof. I think the big mistake that both atheists and theists make lies in the article: it is a category error to think of THE burden of proof, as if there were only one burden that must be borne by one side or the other. In any argument, burdens of proof shift back and forth, which is why not only prosecutors but also defense attorneys introduce evidence into a trial. Theists can easily place various burdens of proof on atheists; happily we can just as easily meet those burdens.
One of the reasons atheists often state their position as "lack of a belief in any god" is not to escape THE burden of proof, but rather to correctly place the initial burden of proof on the theist.
Most of the basic theistic apologetic arguments — especially the first cause and design families of argument — do in fact place a burden of proof back on the atheist. The world — and especially the terrestrial biosphere — really is complex, that complexity really does calls for an explanation, and we know that prosaic intelligent activity (i.e. human endeavor) really does produce astonishing complexity. The design argument ultimately fails, but it successfully places a burden of proof on an atheist.
It is important to acknowledge that the design argument really does place a burden of proof on an atheist: it's a burden that an atheist can cheerfully bear, because it can and has been met. We must make a positive argument to respond to the argument from design, and we can make a positive argument.
There are three families of positive argument: Hume makes the first two with reasonably good rigor: First, the world (and especially the terrestrial biosphere) exhibits features radically and deeply inconsistent with intelligent design; we must posit an "intelligent" designer of either astonishing incompetence or mysterious abilities (a mystery is of course the very antithesis of an explanation). Second, the complexity of an intelligent designer calls out for just as much explanation as the complexity of the world, an argument that Richard Dawkins summarizes in The God Delusion. The third family is of course the scientific theory of evolution, which explains the complexity of the terrestrial biosphere; indeed it explains not only the appearance of "design" but also the appearance of "incompetent" design.
They may be very weak serves, but it's important to emphasize that the standard apologetic arguments really do serve a burden of proof to the atheist's court. The standard atheist philosophical training consists of learning to anticipate and return these serves. We do not escape our own burdens of proof, we meet them. It is the theist who is unable to meet his own burdens.