Are GMB right to suggest that greys should change colour when rendering intents are changed ?
It doesn't sound correct to me.
It's a complicated issue, but yes, it is reasonable that a profile might shift the gray axis among the different intents.
Imagine that the darkest patch that your printer can print on a given paper isn't neutral (it rarely is). Then the question is, how should this patch be handled by a profile? Is this considered neutral black, or is it considered a non-neutral color that happens to be darker than the darkest neutral gray? In other words, the point I'm making is that there is freedom in interpretation of exactly "what is the gray axis". There's not a clear-cut answer here. If you want the black (LAB (0,0,0)) to map to the darkest neutral gray in the print, then indeed you may get very neutral grays but then have a disappointing d-max. Conversely, if a profile maps LAB (0,0,0) to the darkest tone the printer can produce, neutral or not, then you'll get excellent d-max but the shadow grays may get shifted to be non-neutral in order to make this happen. As I said, it's complicated.
The short answer to your question is that, yes, it is entirely conceivable that the definition of the gray axis may change between the various intents.
The practical advice is to make test prints and determine which best suits your image ...