It is actually safe to clean circuit boards with plain water.
However, before you re-power the board, all water and residue must be removed with no dampness at all.
Alcohol is actually much safer than water because it evaporates faster and leaves less residue. Usually it does not matter if it is 70% or 90% alcohol as long as it is completely dry before it is powered up.
Some older manuals recommend isopropyl alcohol especially for things like magnetic recording heads, as it does a better job of dissolving relevant residues and less chance of rusting the steel surfaces. In this case, 90% or higher isopropyl alcohol should be used.
The only reason to avoid water is if iron or steel is present, in which case there is a chance of rusting, and water should be quickly dried off, but even then, rust is not likely unless the device is soaked or some drops are left behind.
It would actually be OK to power up a board if it had pure deionized water on it as pure deionized water will not conduct. However, water does not stay deionized, and tap water frequently contains enough contaminants to be a conductive electrolyte. In these conditions, water can short out the circuit board in unexpected ways that can damage the board, and even if that is not an issue, its electrolytic properties combined with current between contacts can cause corrosion which can very quickly damage surface mount components. If it is dry when powered, this is not an issue.
Some devices (besides the circuit board itself) could be damaged by water, especially if they are water soluble or there is a chance they could absorb water in a way that it can't be dried. Immersing a board or using excessive liquid (water or alcohol) is not a good idea as many components (like electrolytic capacitors and speakers) can be damaged by any liquid.
For some surfaces (like computer screens), water is actually the recommended method of cleaning, as things like window cleaner can damage the anti-reflective AR coating on the screen. But then, some care must be taken to not allow drips to drain into the bezel where it could collect and not be wiped off.
Chemicals like professional contact cleaner are designed to remove nonconductive tarnish and oxide layers while leaving behind a protective residue on metal surfaces that is still conductive.