I would agree that part of the break-in is the user adjusting to the sound of speakers. Yet I'm not willing to doubt that there is some benefit to break in for any pair of speakers based on one test. The author does admit that he's testing "typical electrodynamic driver's operation as seen largely from the mechanical side." He's focused on testing the suspension. Are the Outlaw subs atypical in any way? With Macstatic's RC-10s, they do have Kevlar cones. Perhaps there is something about the material science of those materials that benefit from break-in?
Here's an interesting quote from another discussion about break-in at The Amp Garage
"The other mode is the cone "nodes", which is areas of the paper cone that flex distinctly from one another, in response to constant or transient music information. This means waves of a sort, that move across the paper, or along its length. The paper cone behaves not so much like a piston, but rather more like a waving flag, or an Australian wobble board. The areas in the paper that must flex to allow this to happen will also become looser and more flexible over time, presumably this would make the speaker sound even more open and musical. This is pretty esoteric, I know, but it is a known effect in the violin world as the reason that a much-played high-quality instrument "settles in" and becomes alive after some years. As far as I know, the only way to work that angle is to play varying music through the speaker to get it "used to" the frequencies of music, and in particular the instrument it is intended for. "
It doesn't seem like the Audioholics article is testing for this. Where this effect (if it exists) might have an effect is when a speaker is producing multiple different notes at once or in close proximity to each other, not just some sine wave test.