It's impossible to prove a negative. The test was: "is there evidence for headphone output changing over time" and there was not enough evidence to show this by the author's own admission.
Given the ocean of audiophile bullshit out there, it's not unreasonable to take the default position of assuming a claim is bullshit until there is substantial evidence to the contrary.
And the test was positive, given the test parameters. The author didn't want to extrapolate beyond that (I attribute that to the author's own biases against break-in: "I rarely hear break-in", "voodoo" when referring to break-in), which is their prerogative.
Not to mention that by their very criteria, "all I'm looking for here is a clear trend where the data changes smoothly from the start to the end reference", it did happen.
However, theirs is not the only test out there which shows differences over time. In my limited googling, the consensus seems to be "headphones do break in, even if the effects are limited".
http://www.wired.com/2013/11/tnhyui-earphone-burn-in/
> Shure has tested some thoroughly used pairs of its E1 earphones, which first launched in 1997. And guess what? They measure the same now as when they came off the line. In fact, during the 15 years Shure has been actively selling earphones, its engineers have reached the same conclusion again and again: The sound produced by these tiny transducers during final testing is the same sound you’ll get in a day, in a year, and in five years… unless something goes wrong.
Since there was only one test of one pair with no control, we don't know if the difference is a manufacturing variable, a testing error, or something else.
I don't know enough about statistics, are the differences shown by the author statistically significant?