There is not empirical evidence to support it. Here is some evidence.
In Lebanon, people were given unconditional cash grants comparable in size to basic income. Those above an elevation line got it, those below didn't. This created a natural experiment where the only variable was getting or not getting the money. Result? There was no effect on rents.
In the 70s experiment in the US, the cash resulted in a 4-6% increase in home ownership. That reduces upward pressure on rents.
In Mexico, I suggest just reading this next.
Also keep in mind that as long as the UBI is a flat nationwide rate, it essentially puts landlords in high CoL areas in competition with lower CoL areas.
There’s nothing but empirical evidence to support what I said.
The first example you gave was from an experiment that gave money to some people. This is a non-UBI and therefore sub-sufficient for proving the viability of an actual UBI. It’s the same mistake that they made in Finland.