I'm trying to visualize this problem, (from empirical observations, it may not make sense at all, feel free to ignore or disregard)
XYZ space is absolute, is not relative to viewing conditions.
A specific illuminant define a white point vector (be it D50, D65, etc)
Different illuminant vectors or white point vectors are not parallel but angled between each other.
Color spaces are volumes that are not necessarily orthogonal to XYZ, and are associated to a specific white point vector, and with the vector and color space we have a white point coordinate in XYZ
A Viewing condition is similar to position the observer just in line with a white point vector. In this case, any XYZ coordinate along the white point vector is neutral (R=G=B).
If from a viewing condition the observer looks at any point along the white vector of another illuminant, it will perceive non neutral colors (Even if in the color space belonging to the other illuminant R=G=B)
This may be the case if our viewing condition is D50, ProphotoRGB, Here R=G=B will look neutral. If from this same position we look at AdobeRGB D65, then the values of adobeRGB R=G=B will not be perceived as neutral
It is like both color spaces where not aligned, and in this case it happens that the blue primary of AdobeRGB is outside of the gamut of ProphotoRGB.
For simplicity and practical purposes, the solution apparently implemented in common color conversion tools is to align both spaces so that the white point vectors are parallel or aligned. I think of this like a "rotation" of one color space to align to the other.
As I understand, the standard practice is to align all color spaces to D50 (It could have been D65 or any other)
When you "rotate" or move a color space (which is my interpretation of Chromatic adapation) some colors that where inside its gamut, are now outside, and vice versa, colors that where outside of the gamut are now inside)
For example, original blue primary of AdobeRGB D65 is now out of gamut in AdobeRGB D50 but it may be the case ( I have not done the calculations) that the new Red primary of AdobeRGB D50 was previously out of the gamut of AdobeRGB D65
Doing conversions from one space to another is now easier, since R=G=B is neutral for both spaces now.
So, if you keep adobeRGB with white point D65, its blue is outside the gamut of ProphotoRGB D50. it is only when you do chromatic adaptation of adobeRGB to D50 that it is completely inside of ProphotoRGB. This is the way that most current applications work and it is the practical way of handling color conversions at present time.
Now, I think that we should discuss about how color management should evolve, how future applications should handle color management instead of arguing if a color in a specific color space is inside or outside of another color space.
Some posters like Iliah have pointed out interesting comments and references about this.
Hope I didn't annoy anybody