A bunch of Boyscouts mixed box cake mix, canned blueberry and other ingredients for a cake then put it in the refrigerator for a week before cooking

If you're looking for a technical explanation of why it was disgusting, here are two reasons:
The chemical leavening in the mix (baking soda, which reacts with acid, or baking powder, which is a mix of baking soda and a dry acid which react when water is added) releases carbon dioxide gas, which forms little bubbles in the batter that also expand in the heat of the oven and thus leaven the cake. If you mix the batter up too far in advance, the reactions go to completion, the bubbles dissipate, and the cake doesn't rise.
A very long rest of the mixed up batter may have also allowed the gluten in the flour to develop so that the cake was tough. Gluten is a protein that when mixed with water can align with itself in a way such that it forms the elastic structure that you want in bread, but that seems tough in cake. You can speed this up by mixing it vigorously (as in kneading bread dough, or overmixing cake batter) but it happens on its own at a slower rate without mixing. A week probably gave the batter plenty of time to get tough.
These are all problems somewhat specific to this situation however -- there is no blanket reason why premixing would *always* be bad. A week is long enough that some things would spoil I guess.

Reminds me of the summer when my 12-year-old campers discovered surface tension and conducted "experiments" with the bug juice at every lunch and dinner (breakfast was exempt only because there was no bug juice served at that meal).
You maý find, later, words to describe your reactions.
In the mean while, I suggest tough love and some rules on food experimentation. Examples (or make your own rules):
• Who has to eat the results
• Who has to clean it and surrounding food in the fridge
• Weekly or monthly volume of foodstuffs permitted for "science experiments" or "recipe development."
I sympathize, I really do.