I wonder, will this be taxed the same as lottery winnings? Or is this post-tax $1000?
There's no shortage of frameworks and differing philosophies on the matter of taxation of the UBI. But generally speaking, no, the $1000 would be considered tax-free as for all intents and purposes, it's a gift from the coffers of government's treasury.
Income generated outside of the UBI however, is taxed because well.. it's income and not a gift.
If the income is truly universal (i.e., not means tested), then it will almost certainly be taxed so that higher income individuals pay back a higher percentage of the income.