I don't agree with this, at least not all the time.
To be sure, I've experienced ear shock on first putting on new headphones but gotten used to them in a very short time - that's just getting used to them
I've also heard VERY BAD headphones turn into very good headphones with "break in" or whatever you want to call it. For example, my HiFiMan HE-500s sounded like absolute poo when I took them out of the box
Rather than send them back immediately, I hooked them up to my amp and played my music collection (on shuffle) on them over the weekend - WITHOUT listening to them at all (I was out of town). When I came back on Monday and tried listening again, the difference was literally night and day; i.e., the difference was NOT subtle. They literally sounded like different (and much better) headphones.
I don't believe in break-in for most components (other than very quick charging of capacitors, tubes warming up, etc.), but physical devices like headphones and speakers are in a bit of a different realm, I believe (and, no, I don't have measurements to back it up).