RAW data are not image data in what your computer can display, they are of what all the light sensors have measured. These measurements need to be converted, that's what the RAW converter in the camera and in software like Photoshop, Lightroom etc is doing. This conversion is not just a simple 'left to right' but also an interpretation of data based on sensor characteristics. So there are a lot of factors that influence the way the image is created that you will see on your screen. These factors can be adjusted. In Lightroom it is done in the functions of "Camera Calibration", Photoshop and Adobe Camera RAW have similar functions.
The question is not whether the colours are better when using software. Using RAW gives you more possibilities in editing your images because RAW contains ALL details the sensor has captured. Every pixel still has all data. In contrast, JPG is a compression algorithm that deletes information which are not required to reproduce the image on a computer screen. As a result, these details are deleted during the in-camera conversion, irretrievable. The level of data loss depends on the compression settings and the Picture Style. Extreme example: Take a picture with setting your camera to B/W. All colours are gone in the JPG file, no chance to retrieve them. Use RAW and all data are still there, only the embedded JPG image will show the B/W image.