This may or not be true. There are countless adherents to each side. The manufacturer of this particular piece believes the capacitors especially need time to break in.
There are changes which happen in nearly all components, however minor, at both the physical and quantum levels, and whether or not they effect signals in the audio range and at audio levels is only partly predictable. Because of the high number of variables involved, it is generally difficult to predict exactly which parts, and to which degree, and the ultimate effect on the sound, but things absolutely do "break-in".
When I worked in high-energy physics research 25 years ago, nobody in their right mind would think of energizing a power system designed to run at 120,000 volts at it's full operating potential without "conditioning" the circuit components (i.e. - break-in). We'd start out at 10kv, and gradually work our way up -- generally over the course of days, and only then would full power be applied. These procedures were also performed whenever a system was taken down for maintainance -- whether or not any components were replaced.
Capacitors definitely break in, inductors to some degree, vacuum tubes for sure, and different solid state devices to different degrees.
As to the question of whether it is my ears breaking in or the component, it is probably some of both, but I have most definitely run amplifiers into dummy loads for 200 hours or more without listening, only to then hook them up to speakers or headphones and discover a completely different sound.
I'm sure any of you who bought a new Clari-T and kept it for 100+ hours or more can absolutely say that the amp with time on it was a totally different beast from the factory-fresh one. No?
-- Jim