The statement you're responding to seems to suggest that if we hear two sounds and decide on the basis of our ears that the first is louder than the second, but then measure them scientifically and discover that the second is actually a small percentage of a decibel louder than the first, we should still call the first "objectively" louder. So self-reported human human experience is now "objective" and the results of scientific measurement "subjective". 
We need to remember that these are not in themselves value-laden terms. Objective judgments are not "better" than subjective ones. Indeed, in music (as opposed to the science of sound) it's ultimately only subjective ones that matter. But good quality sound analysis equipment properly used doesn't make elemental mistakes like this. If it says that one sound is 0.1db louder than another sound at the place of recording, then that is simply what it is.
What it DOES show is exactly what you say here and I've been saying all along (and which is such a universally recognised fact in all areas of music and acoustics that I can't believe it's even being treated as controversial): that there are more things contributing to our experience of the loudness of music than sheer decibel level.
spectrum analysis...is rarely useful in music. As you were. here, knock yourself out!
https://www.dept.aoe.vt.edu/~aborgolt/aoe3054/manual/inst4/index.html (first sentence talks about probing. Need I say more?)

Pianists and musicians have plenty of resources for learning and improving in piano, and controlled tone is one of the objects that suggest improvement in piano. In fact, we may have more than Beethoven did, seeing as we now have Beethoven to learn from and many that followed after him!
Math is great and all, but if you tell me I sounded louder than the other guy or here's a funny one. My mother commented on my performance of the chopin valse no 69 no 2 and said I take the high notes prettier than Rubinstein's particular performance in recording. Funny, once I corrected her and said "it is the piano and where it sits in the room", I asked her if she remembered what she said, she reminded me: This valse played on this piano sounds so much prettier in the high registers! (Please, let's just kill any magic left on this planet!)
Also, people keep ignoring my point about the pianist's point of view, sitting infront of the keyboard, visually absorbing mechanical functions of the piano,
synchronizing movements to sound! where as the audience hears sound as it expands and fills the room (hopefully) and just sees the pianists' hands moving, in less or more detail per person or visual focus not influenced by
synchronization of sound to movements, logical, linear, whatever!
My bit about studio recordings and live performance recordings: We were talking about halls, actually. And, you did mention studio recordings. I was not trying to impose but to make an obvious comparison by forming a very subjective point of view...apparently.
When it comes to touch, velocity and (timbre/please say this word with a TEXAS accent!), I guess it depends on where and when you are measuring the frequency content of the total sound coming from the piano, if you are measuring time at rest, too!...but based on one same note at same velocity (and 2 different pianists

?)...I would suggest that it is timed, and the pianist starts with the hand already on the note, at rest. then he is given 5 seconds before he is to press the key, at any volume he may please but at a given velocity. (wait, velocity?)
Pianisnts dont say, "oh, I am going to play this note at 60km/decade."
Maybe rate of repetition? IDK I am actually going to read over what I am responding to, again. Then edit my reply once more. 1 sec
Objective views just don't always line up with subjective ones, that's all. There is nothing that pisses me off more, than having to think about velocity of a pianist...and how velocity of a pianist's hand is different than the velocity of a pianist's finger and how much faster is it than his/her kidney...