You are correct that going from 14 bits per photo site on the sensor to any RGB bitmap loses some data. Raw development always discards data, but the raw data is not pretty to look at. Some sort of interpolation must happen during raw development. If the RGB bitmap being produced is 16 bits per color channel, then less data is lost than if it is 8 bits per color channel assuming that the scene being captured is high dynamic range or has a large number of colors and assuming that the photo sites on the sensor were able to capture that much noise free data. Only that which was captured might be lost. If a large number of individual colors or a large dynamic range were not captured in the raw data, then they cannot be lost.
You are incorrect that the process of JPEG compression always loses data. The JPEG standard has always included an option for lossless compression, but not all software has implemented it. It depends upon the software used and the options specified. I have no idea what photoshop does. I can easily discover what gimp or graphicsmagick does because I have the source code and can look at archived developer comments.
Since the original subject was downsampling to reduce noise, it is given that data will be discarded. The point is to discard as much noise (measurement error) as possible while keeping enough good data to make an attractive image. Thus, the order in which steps are taken is important as well as an idea of how the final version of the image will be used. The noise reduction methods that work with downsampling include median filter, trimmed mean, and gaussian blur. For film, the only one of those methods that was available in the old days was gausian blur followed by unsharp mask and then printing to a smaller piece of paper, but this accomplished something similar.
Here is a simplified explantion of downsampling an image: https://www.cambridgeincolour.com/tutorials/image-resize-for-web.htm with some mention of the various algorithms.
If instead, one wished to produce a high dynamic range image, then one should never go from 16 bits per color channel to 8 bits per color channel.
It appears to me that quality "10" in DPP maps to the JPEG lossless compression or to such a high quality setting that there is no noticeable loss if information, in contrast to the in camera JPG file which always discards data even at the highest quality setting. DPP will use all of the settings that produced the in camera JPG and save a higher quality version of the same image if one does nothing in DPP but open the CR[23] file and save the JPG file at level 10 (I assume this is because more time and a more powerful CPU is available on the computer than in the camera).
Also, I found information on the bicubic interpolation method that I remembered:
https://en.wikipedia.org/wiki/Mitchell%E2%80%93Netravali_filters
This chart shows the tradeoffs, but they are more important for enlarging than for downsampling:
<disclaimer>I am old and I have forgotten much. One would be wise to research this for oneself instead of trusting my memory</disclaimer>
@ebiggs1 wrote:Plus the camera also deleted data if the original photo was saved a s a jpg.
It is true you have me at an intellectual disadvantage about down sampling since I have only rarely done it in PS.
I do know how jpg work.
"You are incorrect that the process of JPEG compression always loses data."
Every time a jpg image is saved, compression algorithm is run to reduce the file size. This means that some data is lost every time you make a change to the photo and save it. The point is, you don't know what data is discarded. You hope it is simply unnecessary close color matches. That is what your tolerance settings do.
Although I doubt I will ever use down sampling as deeply as you have become, I do thank you for the info if I ever do need to.
I went from knowing very little to knowing a very little more! 
