When it comes to the flatness of a frequency response in speakers or headphones, the debate gets hot every time.
In my opinion, you can look at a frequency response from two angles: technical way or psychoacoustic's way.
Former is based on mathematical models and empiric experiments that delivered equal loudness contours from which Fletcher and Munson's are the one mostly taught in schools, due to being one of the first. We rely on ISO 226 standard that is currently the only independent standard we have and was derived from 12 prior independent research. The fact is that at 80dB in low mids the standard has a tolerance of almost 10dB. So it's a very vague way of pinpointing what is flat and what's not. Hence I recommend making a decision by testing the headphones you're looking into.
The latter is a bit less scientific if you wish or at least less mathematical. It's based on research with users and compiling their feedback into a curve that gets revisited every once in a while. That's how we approached our development and that's why we are comfortable stating we have a flat response headphones product line.
Almost every company making a playback system will have its own contours that they trust.
In our case, HPS S4 and S4R were measured using a curve supplied by Mini DSP and smoothened with the psychoacoustic filter provided in REW software.
We did that to represent the flatness efficiently.
We researched the flatness of our headphones during development with our ambassadors.
So they got a prototype model S2, S3 or S4, depending on how far in development we were at the time of their application to the trials. We conducted interviews and collected information on what needs to be changed to achieve a true studio monitoring headphones. The model S4 is very close to what is desired or considered as a perfect response for the majority of engineers. We're continuing to innovate and develop new acoustics for the S5 model that will hopefully bring us even closer to our goal.
I hope this clears what we mean with our statement "Flat out of the box."
If you have something to add to this or have a question, write to firstname.lastname@example.org