A $20k poverty threshold is for a household of 3. For 1, it's a little under $12k.
The argument for a basic income is that one should be able to live comfortably and not just cover bare essentials. This means that people shouldn't be living at the poverty line but well over it. This shouldn't be a disincentive to work because most people need to live their lives around some kind of structured activity. Though it does mean that if there is a shortage of jobs then the unemployed won't be left to rot and the option exists to do some meaningful volunteer work.