I am far from an expert but I believe that whoever said that pure water is dangerous in mistaken... kind of.
Basically super pure water, in theory, can hurt you (or a fish) but ONLY in theory. The reason is that a cell uses osmsis to regulate itself and it is used to impure water. Pure water is nearly a perfect solvent and will enter the cell too fast and could either burst the cell or make the cell permeable to everything. Either way, the cell dies.
The reason this can't happen is because it is too hard to maintain pure water. For a person drinking it, they would have to have no food or other liquids in their body. Also, dead skin, saliva, stomach acid, etc is enough to impurify the water if you haven't eaten or drank in weeks (and was miraculously alive enough to purify water and drink it). Your fridge can't make water that pure anyway and outside of a lab you souldn't maintain this water long enough to get it to your lips or in your tank.
An Ro merchant might put a lable on it just to stay on the safe side or because the materials used to make the product are not aproved for human consumtion. Not necesarily dangerous, just no fda inspection. To sum up, RO/DI is not inherently dangerous.
Yes you can use water from your fridge although you will start to use up your filters really fast.
