To construct a trivial example, say we give every citizen $2000 a month in post-tax basic income. Of course, most citizens have jobs and other sources of income. To make math easier, assume this government has a flat income tax of 20% If you earn $0, you are pay $0 in tax and get $2000 in basic income. If you earn $9000, you pay $1800 in taxes and get $2000 in basic income, netting you $200. Basic income washes at $10,000, and after that serves only to defray your tax costs until it is hardly noticeable.

I can't speak to what levels of taxation and basic income might be useful -- these ones have been selected for convenient math -- but that's the general idea of it.

Or, in terms of your water metaphor, if one person in ten is thirsty, we give water to all ten, but we also take from the nine, so they actually see a small loss. The water didn't come from nowhere.