The key here is the embedded document profile. Numbers are specific to color space. The same visual color will yield different numbers with different document profiles.
In a given file, the embedded profile overrides your working space. But when there is no embedded profile to use, the working space is used.
This means that the info readout uses your working spaces to calculate other modes. So the CMYK readout for an RGB file will be according to your working CMYK.
These will be the same if, and only if, the profile you want is the same as your working space for that mode. If not, they won't match.
One more thing: If you have special content in the K channel that is not part of the image, like overprinting text or graphic elements, this will be integrated into RGB data and you need to recreate it from scratch.