It's true but what's allowed varies with the RI.
Again, I can't understand how an ICC profile knows anything about image content. They don't even 'know' anything about an adjacent pixel do they? IOW, they examine a pixel value alone and convert it based on a number of assumptions perhaps and a lot of data is a guess (by the time the output profile comes into the scene, the data is usually in Lab, the source color space is unknown). IF an image is what I understand it to be, I still can't understand how a profile knows anything about it to alter a conversion based on content. Confused.....
WE humans need to view pixels in context and view what really IS an image and decide what RI to use based on those pixels and color in context no? That's why we toggle the RI's and select the one we visually prefer. We humans that wish to control this mapping have to use a full color managed path which includes soft proofing and control over the rendering intent if we desire this kind of control. Going full circle as to why Printer Manages Color is a black box approach with less control for the image creator and/or print maker.