Sound canceling headphones reduce SPL?

I am wondering if sound canceling headphones reduce the SPL in your ear canal. My understanding is that the headphones use a microphone to survey the ambient sound and then "replay" the inverse signal of that sound while playing the signal from the playback device. In theory delivering two signals at once. If one where to be in a 90db environment and turned on noise canceling headphones you wouldn't hear anything but would there still be 90db acting on your ear drum? Or since the headphone is producing the inverted signal it therefore is canceling out the 90db and your ear drum has no pressure acting upon it? If the latter is true i wonder why no one has developed an ambient noise generating speaker that surveys ones room and then produces the inverse of the signal, eliminating all exterior noise from the equation allowing the listener to hear only the stereo. While keeping the SPL low as too not damage or fatigue ones hearing. Any thoughts or technical descriptions would be appreciated.
Noise canceling headphones were developed for aircraft pilots who need to hear ATC clearly in a noisy aircraft environment. They will never be audiophile-approved. Why? Because the best ones (by far) are made by Bose!