Though your meaning is clear enough, strictly speaking there isn't really such a thing as a 'true EI', because the EI is simply calculated from the light intensity at the plane of the sensor and the exposure time. It doesn't matter what the result of the exposure is. The ISO speed is equal to the EI (rounded to the nearest third-stop in the standard series) when certain conditions are met in the recorded image. For a digital camera there are two main ways of arriving at the ISO speed: saturation-based and noise-based. If you like, you could call the saturation-based speed the true ISO speed.
The saturation-based speed is calculated from the exposure that would reach the upper limit of the capacity of the sensor or circuitry (ie on the verge of being blown out), and it is generally the method that is used for the highest quality.
It is fixed so that in effect an 18% grey will give an exposure that is 12.8% of the exposure that would result in saturation, or to put it another way, a 100% diffuse-reflective surface will give an exposure that is 71% of the exposure that would result in saturation.
Best,
Helen