Standard computer RGB is 8-bit per RGB channel or a total of 24-bit color, which adds up to 256 levels per channel totaling 1.7 million possible different colors. Add half again as much depth to each color channel and the total number of colors is more than my little calculator will display.

In practical terms, when saved a 12-bit per channel or as you correctly assumed 36-bit RGB, in Raw format at the capture depth you have a file with lots of room and flexibility (large gamut) to adjust to an ideal level and then when reduced to 8-bit per channel RGB to make a print nothing is really lost in terms of what can be reproduced. If you started with just 8-bits then changes in contrast, brightness, saturation and balance would push some data out of gamut and you would have less than a full gamut to print which would result in poorer print image quality.

To reinforce what David has said. When you capture in 8 bit, converting to a higher bit (like 16 bit in Photoshop) doesn't add data that wasn't there when the capture took place. If you have captured an 8 bit file, like a JPEG, you are stuck in 8 bit land forever with the file. And if you do capture a 16 bit file and do your editing without converting to 8 bit, you'll find that Save As to file formats that don't support high bit (like JPEG) are not available.