From my reading, they would say some particles are just much more energetic than usual (for some reason we are ignorant of). See the post above about flipping a coin. According to the statistical model we use for coin flips, it is really unlikely to flip 100 heads in a row but not impossible.

Wouldn't it be possible to see this experimentally? You'd find particles jumping out of a "potential energy well" which they shouldn't be able to escape via tunneling.