This week I was listening to a piano recording that didn’t sound much like a piano and I began to wonder about the relative importance of two issues of speaker accuracy. I am naïve about high fidelity systems so let’s assume for the moment that all amplifiers are perfect and that we are evaluating an amplifier / speaker system.
Welcome to AudioCircle proteinchemist. Great first post.

There are many problems along the chain, from an event (live performance) to final reproduction (your speakers playing back).
Right from the onset, piano's are generally recorded from an improper perspective, with the results sounding unnatural. Recordings of piano are often done with ambient (far field) and spot (nearfield) miking. The spot miking is where things get askew. They often aim (one, sometimes 2 mics) aiming down at the soundboard in an effort to highlight the piano better. The only person that hears the piano close to that, is the player, not the audience.
Do the sound characteristics of some systems differ as you change the volume control?
Yes, most definitely. I think Duke's post

is a great explanation, and I can tell you that in practicality, the SPL level you mix a recording at, has a lot of bearing on how an engineer will shape the sound due to exactly what Duke explains is happening as SPL increases.
Room interaction (room acoustics) also play a huge factor. Comb filtering and room gain affects on bass response as SPL increases are important factors to the overall tonality of a speaker.
The ear itself has non linear characteristics with frequency vs SPL. Fletcher/Munson plotted curves many years ago on human hearing, and there are other more current studies.
A little know fact is that many engineers have bad hearing from years of exposure. A major industry publication years ago did hearing tests of recording engineers under strict anonymity, and the findings were alarming. Many of the engineers had severe losses at particular mid frequencies.
As far as compression added during the recording, in the case of a classical recording, it would use
limiting and not
compression. Limiting (hard or soft)is compression above a certain db threshold (usually high, in order to prevent overload or clipping), whereas compression is when you compress at a low db threshold and decreases the db gains (at a user adjustable preset ratio, ex: 4:1) of the entire performance. Compression as properly defined, is more of a pop recording (and it's abuse has become a popular sound shaping )technique, and would not be used (for the most part) in any classical recording.
There is also tape compression. As the db level approaches oversaturation levels, tape begins to compress the signal. At oversaturation, tape distorts and compresses severly.
richidoo is absolutely right about the importance of a low noise floor. It's an easy way to increase low level resolution, and avoid SPL related non linearities in the audio system.
Or am I straining at gnats and swallowing camels?
No, most definitely not. Very good questions.
Cheers