Rent prices are still governed by supply and demand (modulo some rent control), not by how much money the tenants have.
This is not accurate. Rent prices have little to do with supply and demand, and are primarily driven by how much money tenants have (or more accurately, how much tenants can be bled for before they give up and leave).
This is why rent rises even when supply is greater than demand, and why rents rise even in places where demand is falling dramatically.
How else do you explain housing costs being lower in Austin (available land, less restrictive zoning) than New York City despite Austin having a higher median income?
That's demand.