I think headphones do burn in, and whether or not they do, there is a much more plausible mechanism for them to break in than something like solid state electronics, so I think the position is justified until more hard measurements come in. Headphones have moving parts, and the properties of those parts can be changed by repetitive movement, just like breaking in a new pair of shoes. I doubt anything actually does take several hundred hours to break in though. If anything did take that long to break in it would likely either sound awful right out of the box, since it requires significant loosening up, or else it would sound fine out of the box and any changes that occur over time would be very small because the diaphragm was very tough and took longer than normal to break in.
I also have a data point of my own, that points against a purely psychoacoustic explanation. When I got my DT990/600s I thought they sounded great right out of the box. By day two, something seemed a little of and it was soon clear that the highs were far to high for my tastes. Maybe it was just what I was listening to, so I listened to the same albums I listened to on the first day again. Well, I tried to anyway. I couldn't make it more than a few songs through most of those albums. The treble was grating on my ears. Then I found someone else on here who had the same problem with his. They started out great but the treble just kept creeping upwards. I really wanted to keep them though. I wanted to like them. In fact I like everything else about them. The bass, the soundstage, the detail, it was all great but I couldn't stand the treble at all.
I decided to give them another 100 hours of burn in before I decided to return them or not. I used music, pink noise, white noise, sine wave sweeps, and even a 25hz or so rumble. I tried listening to a few tracks every 24 hours or so and it seemed to be getting even worse, but not by a large enough margin to know I wasn't imagining it. After they'd racked up about 125 total hours I gave them one last try with the same tracks I used when I first opened them. At first it seemed so-so. Not as good as fresh out of the box, but not quite as bad as I remembered earlier. Then, suddenly *VIOLIN SOLO* and I nearly fell off my bed as I hastily reached for the volume control. That definitely didn't happen the first time I listened to that song with with those headphones a few days ago. It was decided. They were going back.
The psychoacoustic hypothesis of burn in explains why someone may like a headphone better after getting used to it's sound, but it does not at easily explain why someone would like a headphone at first but quickly change their minds. I'd also like point out that the only change large enough for me to be reasonably sure I wasn't imagining it occurred very quickly compared to most burn in recommendations. It was certainly less than 10 hours of use, and probably less than 6, though I don't remember exactly how long.
Based on a little bit knowledge, logic, and personal experience, its my opinion that headphones some do in fact burn in but that the process takes place over tens of hours, if that. Certainly not hundreds of hours. The DT990/600s are the only 'phone I've noticed such a dramatic change in though.