I regard a camera as principally an image recording device, able to make a record of light in a moment of time. The matter of reliable colour reproduction is rather more complicated: I understand that museums and art galleries sometimes use multiple monochrome images and colour filters in order to accurately record colours for posterity... Therefore, wishing for reference colour from a camera could be big ask!
When film cameras were the norm, achieving even reasonable colour was a challenge for the enthusiast. Kodachrome slide film helped reduce the number of variables, but still left correct exposure and light temperature (white balance) up to the photographer. Consumer print film and mini processing labs made things even more unpredictable. No wonder that black and white film was still readily available decades after colour film entered the market.
Digital photography seemed to offer a new freedom for enthusiasts. Using a computer and printer, colour printing could now be done at home -- with better results than the consumer film processing labs. Photographic film and processing became a niche market. And digital cameras should have produced consistent colour results, regardless of the make and model of camera? Er, no, not in practice.
The camera manufacturers realised that most people don't actually prefer realistic colours, and found that by boosting certain colours, the digital results were more appealing. Consumers were inclined to choose the digital cameras that made the colours "pop", rather than the cameras that more faithfully captured the scene they had viewed. People wanted their skies to look blue and their foliage to look green, as well as their people to look healthy, even when they weren't necessarily so in life!
Once it had sunk in that my small collection of digital cameras was not doing as good a job at reproducing colours as I had assumed, I was determined to do something about it -- ideally without having to spending more money. The first thing I did was to make sure that the computer and monitor combination that I normally use to view (and sometimes post-process) my images was calibrated. I have a Mac, so this was easy to do without needing to use an external device and associated software. This helped me to see better what was wrong with my photographs.
To use my colour reference, I position it close to the monitor, and photograph it with the camera I wish to check -- using the Custom White Balance setting adjusted for the natural daylight illumination. I find it helps to increase exposure by 2/3 EV over normal exposures. It only takes a matter of seconds to view the resulting image on the computer, and I judge by eye as to how well it resembles the reference. Then I make a slight adjustment in the Custom Color settings in the camera, and keep repeating the process till I feel I have the closest match. Not very hi-tech, but it works for me... (Fortunately, the compact digital camera that I used here has a limited amount of individual control over red, green and blue colours -- something surprisingly not available in some more expensive DSLR cameras.)
For comparison, I conclude with another photograph of my back garden taken only a few seconds later, using the same camera as before, but this time with the adjustments that I feel produce a more pleasing and realistic result. You are free to disagree of course; but it looks more like my garden to me and I'm happier. Perhaps the greens are still a touch on the blue side though?... (For the record, the camera was a Canon PowerShot S95 in P mode, with Custom Color set to Saturation -1, Contrast -1, Sharpness +1, Red +1, Green 0, Blue -2 and Skin Tone +1. Exposure used Custom White Balance.)