We're talking about basic income for the purpose of ending poverty, not giving people a billion dollars every year for some undefined purpose. Your hypothetical is nonsense.
People who win the lottery often end up worse off than when they started. Giving everyone a multiple of the highest lottery winning every year would be destructive.
No your point specifically is nonsense, because its a false comparison. Having a basic billion dollars would be massive wealth redistribution, as opposed to minor, and would have many additional negative consequences due to the severity of it.
mkr-hn's describing (as I read it) redistribution of wealth.
The problem with your suggestion is that it would necessarily create runaway inflation, because there's no way to square that payout with government tax income.
You can have redistribution of wealth without runaway inflation, there are a number of existence proofs of this.