Theoretical physics shows "irreducible complexity" arguments invalid.

[StuW]

but what's the difference between a statistically extremely unlikely event happening and the possibility of such events being observed?

The amount of observation time.

http://www.exitmundi.nl/eternity.htm

As the quadrillions of years pass by, something very odd should happen. In eternity, even the rarest events get a chance to occur. Weird, bizarre phenomena that only happen once in a zillion years or so, become quite normal.
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In the Universe, this should give some really surprising results. With eternity at hand, the vacuum should begin to yield all kinds of objects. Incoherent lumps of random garbage, most of the time. But on very, very rare occasions, you’ll see other objects popping into existence. The Eiffel tower. A purple camel. A golden parking garage filled with chocolate Cadillacs. Napoleon Bonaparte sitting next to Mike Tyson on top of a stack of comic books. As the googols of years pass by, it’s all there.

Not that I totally agree with what's said, but that seems to be the current consensus.