The main problem with alcohol as a cleaning solvent, is the flammability of the vapors, and the fact that a pure alcohol fire burns with a nearly invisible flame. Note that using a paper towel, and then throwing that in a trash container can allow vapors to collect, and then what happens if someone throws in something that ignites the vapors, or they spill over to something very hot, or a flame. An alcohol fire is quite sneaky, as it is very hard to see. In the US, to meet OSHA regulations in a commercial lab, we were required to have a flammable items disposal bin, and to empty the bin every day into a well ventilated container that was stored outside. We were also required to have a special storage location for items considered flammable. My guess is that the location is trying to sidestep such expenses, by simply saying not to use flammable items there. If it is like most ventures like this, they simply cannot afford the expense and hassle that occurs with flammable materials.
I suggest going to items that are either no-clean, or water clean. Solder, solder-braid, and flux should all be bought that meet their requirements. They are not appreciably that much more, and will reduce the risk of fire from flammable materials. For the vast majority of circuits, the no-clean chemistry items are fine. Some of the no-clean items may leave a small amount of residue, but it tends to be small, and by design is not sticky and is not conductive. If you absolutely require the very least leakage currents possible, use the water clean items.
Regarding your question about water and electronics...
The issue is really about impurities in the water shorting out the electronics. I use an ultrasonic cleaner filled with deionized water to clean pcb's all the time. Pure water is a poor conductor of electricity. It is the impurities in the water that allow current flow. The important issue is that after cleaning, regardless of what solvent is used, to dry the board thoroughly. Note that just because the big flat areas are dry, does not mean underneath IC's and pins is dry. I suggest 15 minutes or so in a warm environment. We used a small toaster oven modified to sit at about 150F.
Note that some components shoud not be immersed. Such items include certain switches, and connectors. Usually items where the capillary action of the water would allow contaminants to be carried into the device, but might make it difficult to dry out easily. For example dip switches that have a sealing tape in place allow for water cleaning, after which you peel off the tape to operate the switch.