Sean,
Thanks for the question and thanks to Bullwnkl999 for pointing you to my article "Why and Amplifier's sound changes when you change the tubes". I started designing circuits by ear (and my oscilloscope) at a very early age, before I had studied electronics formally. I felt then and still feel now that circuits affect sound more than parts. Yet parts interact with circuits, and that's the rub. As a mature designer, I design so that part variations have the least effect on my circuits. Therefore, you may hear the least variation when you swap tubes in Music Reference products.
In the examples given in the article mentioned above, the changes were both audible and measurable and due to circuits which, in my estimation, are too sensitive to tube variations.
Now, does a certain tube, say the smooth plate Telefunken always sound the same in every circuit? I don't find it so. Does a tube have frequency response properties of its own? Definitely not. Can a tube change the frequency response of a circuit? Yes it can, but it shouldn't, not in a good circuit.
Although we can't fix overly-sensitive circuits, we can screen the tubes for operating parameters such as gain (mu) and plate voltage for a standard bias value. This is better than just a transconductance test in a Hickok as it measures where the tube will "bias up" in a typical circuit. I find that the self-bias point is the most important factor in sound as it affects distortion directly. We have rejected many of the recent 12AX7 variants as they do not "bias up" anywhere near the accepted (RCA, Sylvania, GE, Telefunken) values. As those companies used the same published curves (have a look they are all the same), their tubes biased up to the same point (except for tube to tube variations). So I agree with your last statement wholeheartedly. We keep a tight watch on operating points, and even have customers savvy enough to request tubes from the upper end, lower end or the middle of the range, as they know what they like. Since all the data is on every tube, we can easily pull what they want from stock.
With all this information on every tube, why buy random tubes where you dont know anything about the noise, microphonics, gain or operating point.
I'll share a little story on noise. When I was visiting the EI factory in Yugoslavia I mentioned to the engineer that the folks at Sylvania (in Altoona) didn't know how to make a low noise 6DJ8, 12AX7 or any preamp triode. It's mostly a function of cathode coating. When I saw how crude the cathode coating technique was, I wondered how a low noise tube gets made anywhere. They just mix this powder up in a bucket with water and spray it on the nickel cathode sleeves. So I asked the engineer at EI how they got such low noise cathodes (theirs are the best I've seen). He said, "Well we dont know for sure, its not a repeatable thing, we have learned to mix the coating a few days before we use it, it may be the water, it may be that the janitor takes a piss in the bucket at night". Well, they say its the water that makes New York bagels the best. Go figure.