This doesn’t bear out at all. Why would giving everyone more disposable income in dollar amounts reduce rent? First thing I would do if universal basic income was passed (and I don’t doubt I would be taxed at least 10–15% more to get it passed) is increase the rent that I would charge on things like housing.
You’re not increasing the housing supply for the rental market using UBI and you’re giving everyone more money. The same people still need to live in the same houses and the supply-demand curve doesn’t move.
Same supply, same demand, people can pay more. Sounds like an upsell to me.