Think of your recording room for a moment as a giant violin, with you standing inside with your recording gear. Seriously, play along with me on this one.
Commercial violins are usually constructed of maple, with spruce supports, sound post, and a hardwood bridge. These different materials, as well as their shape, thickness, density and arrangement is what makes one violin sound like a cheap rental violin versus a top quality 1870's handmade Stradivari. In fact, even the best of the best (Stradivari) will sound very different in a hot, humid room as compared to itself in a dry, cool room. Even the glue holding it together and its varying thickness along the joints makes an obvious difference in the tone of the instrument.
Your ears respond to this very well, and is why we are able to tell the difference between a good violin and a cheap one, with our eyes shut, meaning no additional information regarding the instrument's quality, construction, etc. You can hear the difference.
Drawing a parallel here, the room you record in colors (with tonal adjustments) the sound in many ways. Add/subtract lower frequences, add/subract higher frequencies. Some frequencies peak and others are cancelled. Harder surfaces reflect more than spongy surfaces, and materials like wood often add beautiful rich harmonics to the sound waves bouncing off them. This is due to the resonance factor of the wood and inconsistancy in the density of most woods.
While you generally don't say "thats a 13th order harmonic from the third plank on the hardwood floor thats been added to the bassline", trust me, your brain can and does interpret this information constantly. Using this same acoustical information, your brain on a constant basis determines your environment for your safety. This is how your brain, while you're lying in bed with your eyes closed, know that a fruit fly went overhead versus a mosquito or a bee or
a yellow jacket. This is how without looking, if you really try, you could estimate distance of a friend talking to you in a normal voice, because you know this friend and how loud/soft that person's voice is.
Recording music is based on the same information, same interpretation, same type of tonal, spacial, etc type of information.
I would say in a technical sense, the room matters greatly, and is probably why this forum is frequented as often as it is.
Hope that helped!