Okay, but there's still more to it, because there's also, surprisingly, a lot of white noise that goes into piano playing. This includes not only finger to key white noise, but more importantly, the noise all the stuff bouncing around inside the piano, which resonates on the soundboard just as the string vibrations do.
Without getting into that too much for now, let me re-state an important question: Who cares? Well, okay, here's something that will never apply to most people, but applies to me: should pianists play chamber music with the lid of the piano raised, or not?
The general, modern consensus is yes: the piano sounds better and "fuller" with the lid raised. But there's an inherent trade-off with balance, because raising the lid also makes the piano louder. When playing with string players, who just can't produce as much sound as a piano, especially with thickly written piano parts, this is an important concern.
For instance, I'm playing the Mendelssohn second cello sonata in a recital tomorrow night, where, on the first page, the ratio of total piano notes to cello notes is about 15:1. We played a practice run-through the other day, with the lid of the piano not raised, and one of my professors suggested that I play softer in order to avoid covering the cello, and raise the lid of the piano. What gives? I think the suggestion stems from a mistaken view of the nature of piano action: that is, that I can play softer, but still have an equally loud of louder-sounding "tone," so that the overall impression of the music isn't lost. (To the professor's credit, a lot of it has to do with voicing individual notes over other ones as well.) However, the main fact remains: for any given timbre of playing, raising the lid will produce a more sound, so as long as covering other instruments is an issue, playing with the lid closed seems like a reasonable response for me.
Of course, lots pianists don't like the insinuation that they can't adequately "control" their sound, and think that playing with the lid closed is an affront to their playing ability. But this just seems kinda silly to me. I'll be playing with the lid down tomorrow night at any rate....