The dream is UBI might slightly increase the cost of some things but it will greatly increase the buying power of those at the bottom. It won't help you afford a city apartment but you can now afford a place to live somewhere.
This isn't proof or anything, I just don't think the bay area disproves anything.
If I’m a rational landlord and the market is efficient: I figure out what percent of income is typically spent on rent (P). If people suddenly get $N more, I immediately raise rent by N x P because the market will now bear exactly that much more. Assume all landlords are as rational and we are back where we started.
This isn't proof or anything, I just don't think the bay area disproves anything.