Well, CMYK is based on a 0-100 scale, unlike RGB which is 0-255. So, there are only 100 "greyscales" in CMYK vs 256 in RGB.
Try "babelfishing" an input RGB value; convert it to CMYK using whatever conversion algorithm you like, then convert THAT back to RGB to get the "closest match". As long as you can then convert this closest match to CMYK and back ad nauseum, you've found an RGB value that will translate 1:1 to RGB. If the color keeps skewing, there's probably something wrong with the conversion, one way or the other. I don't know the specifics of RGB-CMYK conversion, and there isn't just one algorithm.
EDIT: Check the remark at the bottom of this RGB->CMYK converter: http://web.forret.com/tools/color.asp?R=85&G=85&B=68. According to this, CMYK can represent MORE colors than RGB because of the extra dimension of black. I call shenanigans, but I guess it again depends on your specific converter implementation. Wikipedia simply says it is "difficult" because CMYK values are more hardware-dependent than RGB.