that's just factually not true. i'll explain it slowly so you can follow:

rent is determined by two things: cost of construction and profit of the landlord.

cost of construction is more or less constant and wouldn't change if people have more money to spend. profit of the landlord is subject to the free market, i.e. if renting out apartments becomes overly attractive (as in, landlords make more money with it), then new people will enter the market to also become landlords and rent out apartments. since these landlords are all competing against each other, they try to be more attractive to potential customers by lowering their rent, which means lowering their own profit. that's how the free market works.