There is an acoustic signature of a room by itself, by virtue of his vibrating body...
All rooms differ...Even if i tune them, why?
For the same reason that the vibrating body of all violins differ from one another for an educated ear even when they are tuned by the musician himself... They always differ and this difference i call it yes their acoustic signature, their timbre ...
Then the 2 rooms like the 2 violins will produce the same musical tonal playing but with a different sound timbre perception, so subtle the difference could be and will be, the difference will stay...
This is the reason that we only know how sound an audio system in some specific conditions when we tune it ourself with the chosen room ...If we listen to it in another acoustic conditions , it will not change completely for sure, because like for the room which will sound different before and after his tuning , the audio system has his own internal acoustic signature which will express itself differently in different room ... It is his "timbre" expression so to speak...Like a human body can play the same tone than any other body but with a unique timbre expression...
This is the reason why there is no absolute room and no absolutely perfect gear system...No absolute timbre perception either...Perfect hearing of perfect pitch is not the same phenomenon than timbre perception itself...
«Pitch allows us to hear intonation in a language and notes in a melody. Timbre allows us to distinguish the vowels and consonants that make up words, as well as the unique sound qualities of different musical instruments. Combinations of pitch and timbre enable us to identify a speaker’s voice or a piece of music.»
Then pitch perception and production is linked to some precise frequency tone, timbre is a more complex phenomenon related to the resonant human and musical body in an acoustic environment ... Timbre phenomenon cannot be reduced to only a spectrum envelope for example there is also a time envelope and way more related to the interaction with the acoustic environment around the resonant body ...
Pitch perception will not change from a different room or from a different singer body to another one...
Timbre will change from one room to another and from a singer to another one....
In a word multiple trade-off are at play in acoustic/psycho-acoustic ....There is no perfect room, no perfect instrument, no perfect ears, only perfect musical tone yes...
Then your choice of words is neither true nor wrong...I only try here to convey my own limited understanding from my room tuning process...
Remember that i am not a musician nor an acoustician either, i only made listenings experiments in my room...
Then two room even tuned by me cannot sound similar, they own different signatures that i adapted to my own liking or ears/brain signature... If we put the same system in these 2 room, different in size, geometry, topology and acoustic content my tuning will transform them in something i like yes but different...( the audio system is part of this acoustic content of the room and the same system will sound in a different way in the two rooms)
All of what i just said dont contradict the fact that picking between some different pieces of gear in a room tuned by me is a good idea Why?
Because if i tuned the room i will not need a blind test to chose well... If i dont know the room signature it is better with a blind test yes...
My best to you....
Don’t you believe that if 2 rooms are properly arranged for your ears they will sound fundamentally similar but with their own signature?