The DMax comes out differently in the M3 mode, but false relative to what?
The Dmax is calculated directly from the spectrophotometer measurement of reflected light from the blackest patch. With M2 it is from reflected, randomly polarized light. When M3 is used it measures the fraction of reflected light that was polarized prior to reflection off the print. That will be significantly different on most matte paper surfaces and doesn't scale from the white reference white. Interestingly, it makes little difference on glossy papers. It is only accurate if the print is illuminated with polarized light in the same orientation. That's possible to do but can't say I've seen it done.
Additional info:
I don't want to overstate opposition to M3. There are situations where M3 can produce better visual results:
I do believe it's likely to make better profiles (in a visual sense) with canvas. Especially canvas with enough texture that significant specular reflections are present. Canvas presents a particularly difficult profile target in shadows because specular noise is unavoidable. One approach could be to create a larger set of duplicate patches. Scan them and reject the higher luminance outliers but this is tedious and time consuming. Normal use of a single, if large, patch set is not sufficient. One needs to create at least 3, and likely more duplicate prints of the patch set. Further, averaging is sub optimal. It's the outliers that need to be rejected. Just one remaining outlier can easily bump a patch luminance enough to create strange gradient bumps in prints using that profile.
Matte prints with M3 profiles are more problematic - see the discussion of how they are illuminated and the diffuse light (white room) ambient. I suspect M3 provides better results in the latter situation. Especially when comparing to glossy prints in the same setting. The colors should be more consistent between the two in that environment.
Also, while cross polarization is used for M3, it's not necessary for viewing prints from them to use polarized glasses since the light that is reflected is already highly polarized unless coming off things like metallic surfaces. Polarizing the illuminant accomplishes most of the specular attenuation.
Creating profiles using a light integrating sphere spectro would significantly decrease the DMax of glossy prints and drop the profile gamut considerably but it would provide a more colorimetrically accurate print when viewed in the diffuse white room I mentioned in earlier. It's also highly impractical, slow, and expensive.
The ICC recommends not using M3 and I believe I understand their reasoning. However, I suspect it is at least a reasonable choice on some substrates such as canvas.