This is of course correct in principle. But the rest is the practical implementation.
In the dmm noise thread only one 34470a is measured, unfortunately. With the result of 0.01ppm Vrms per range in the 10V range. The 34401a/34461a/34465a have corresponding results between 0.02 and 0.03. Since the noise of the reference is not included in this test, this means that the ADC is less noisy. It must do so in order to meet the linearity specification of the instrument, because the noise of the ADC influences and of course limits the linearity. And indeed, the linearity of the 34470a is specified as 0.6ppm and that of the others as 1.5 to 2 ppm. This is about the same factor of 3 as you find in the noise test.
On the other hand, the results of the linearyity test thread show that the 34470a does not necessarily perform better there. And the noise of the reference is included in these measurements. And the implementation of the reference on the 34470a has also been criticized (Dr. Frank, airflow of the fan over the reference, etc.).
Of course, the measurement of linearity is very demanding and therefore may be slightly inaccurate. On the other hand, even a non-optimal implementation of an LTZ1000 reference can increase the noise. So it may very well be that there is practically no big difference between 34470a and the others. But just more question marks than clarity. And then additional problems like the one of this thread unsettle all the more.
Regards Dieter