The argument is made clearer by fig.3, which paraphrases the Gestalt perception model proposed by Theile. It shows how, in passing through the outer ear, sound is subject to HRTF spectral modification, H(s). This spectral modification is used by the brain to help determine the sound source's location, and then inverse filtering, H'(s), is applied to prevent the timbre of the sound from being distorted. If H'(s) is not the inverse of H(s), as Theile argued is the case with free-field headphone response because the image is not perceived as being forward of the listener, then cancellation is imperfect and, as a result, the perceived sound is colored.
Fig.3 Gestalt hearing model used by Theile to argue against the use of free-field headphone response.
Theile contended that, because the headphone image has no preferred direction, the ideal headphone frequency response would be that which pertains at the ear in a diffuse soundfield, where sound arrives equally from all directions. This diffuse-field, or DF, response is significantly different from the FF response, and Theile went on to demonstrate its superiority in experiments in which headphones were electronically equalized to have either FF or DF responses.
If you suppose that, as a result of Theile's work, there is now a headphone-industry consensus that the DF response assumption is the correct one, prepare yourself for disappointment. Headphones continue to espouse widely differing response philosophies: some close to FF, some close to DF, and others nearer to flat. Which is "right" remains a bone of contention.
From the point of view of those who measure headphones, then, there is no hope of being able to apply a universally accepted correction to generate a "flat is correct" response. The best we can do is apply both FF and DF corrections and hope to learn by experience which, if either, truly correlates with the best subjective performance. Until recently, such corrections were not generally available for artificial ears with eardrum simulators, but recent work by Hammershøi and Møller has plugged that gap (footnote 5). Their third-octave corrections, normalized to 0dB at 1kHz, are shown in fig.4.