A friend, a retired vestibular physiologist, had this reaction when I sent him the link to the Nura site:
"I'm skeptical, too. The reflected wave will contain two components: The dominant one will be a function of the shape of the ear canal and eardrum. However, every person's nervous system will adapt to idiosyncrasies there as the person grows. One's perception of sound is very personal and it changes with attention.
The second component is reflexive. There is a muscle in the ear called the tensor tympani that tightens the eardrum according to the sound pressure level. It is designed to protect the hearing from loud-sound damage. The reflex is very quick (a millisecond or so) and it causes the eardrum to act as a drum head and emit its own sound wave. This will mix with the reflected wave during the measurement they describe. This is a by-product of its real purpose, which is to reduce the overall excursion of the eardrum so that the tiny bones of the middle ear are not damaged.
Tweaking the filter profile with that information will produce an experience that sounds different from the "untweaked" version and some will consider this to be better. However, in our society, the biggest problem is damage to the hearing transducers in the cochlea, usually the result of excessive noise. The human cochlea has about 20k individual transducers arranged along a membrane. Incoming sounds set up a complex motion along the membrane that causes the cilia or hairs to move and thereby stimulate the production of neural pulses. The interference pattern along that membrane and thus the pattern of neural stimulation is perceived as different notes and amplitudes. A single note of 90 dB for two hours is enough to destroy those hairs, rendering it impossible to hear that note again. This type of damage is cumulative. That is why our hearing generally degrades with age. [The Mabaan people of Africa live in the jungle, but do not have any instruments that produce loud sounds. Tests have revealed that they generally live well into their 80s and that their hearing remains as acute as that of a youngster over their entire lives.]
The ear tests that these earphones purport to conduct will only sense the reflected and reflexive waves, but have no way of tracking the nerve damage. The latter requires that the subject indicate when they actually hear the test tone, a procedure known as von Bekesy audiometry. Unless the user of these earphones can be in a sound-proof room and have a button to press during the testing procedure, I do not see how correction for nerve damage can be accomplished. The hearing profile is much more distorted from nerve damage that it is from ear canal resonances and so while it sounds like the holy grail of earphones, I don't believe that there is an actual improvement in fidelity."