The obvious answer here is that basic income won't be evenly distributed to all citizens. A household earning the average national income will get $1,000/month from the government, and see their taxes go up by about $1,000/month. So it's difficult to raise rent on everyone when only a fraction of your customers have true extra income.

Imagine you're a landlord who runs a property for those of normal income. How much do you raise rent because people who currently earn below the poverty line suddenly have $1,000 extra per month? You can raise rent on everyone, but then most of your middle class tenants will move out to seek better prices. The same is true for the price of groceries and other staples.

A smart business will maintain their prices and benefit from a larger customer base. Since everyone doesn't experience an increase in income, raising rents of all forms will only open those businesses up to price competition.