You will not get a definitive answer, as you have already discovered. There are some who say that a solid back lends sympathetic vibration to the top. In other words the sound waves that the top creates make the back vibrate and that creates its own sound. There are others who say that its best to just let the back reflect the sound, and don't want it to vibrate and absorb any, since all vibration has some losses. I would say from what I have read that most agree the sides don't contribute much to the sound.
All that said, I don't think solid backs and sides add much to a ukulele's sound. There are many fine guitars what are purposely built with laminate backs and sides, and makers say they do it for better sound. It is worth noting that the Sailor brand ukuleles have backs and sides made from a sandwich of poplar and cherry, or other woods on the outside, and inside, but they have solid tops. They get good reviews and the two that I have played sounded good to me. I think a lot of what luthiers build they build because that is what people will buy, so there is a lot of tradition that goes into it. Most people (myself included) just will not pay as much for a laminate back and sided uke as we will for an all solid because we know they traditionally cost less. Since most of the cost of a custom ukulele is labor, if I were a luthier, I would probably only make all solid ukes and charge a higher margin on them.
I own and love an all solid mahogany Ohana soprano, but when I was deciding what tenor to make my main player I played a lot of them, both solid and laminate. In the end, I thought the solid tops with laminate backs and sides sounded as good if not better than any of the all solids I did A-B comparisons on.
In other words, I think it is mostly the top that makes the difference. How the luthier puts it all together is also important and a good one can even make pallet wood sound great.