Supply in the number of rental units available is what drives down prices. This is extremely obvious to anyone who visits Dallas or Houston Texas where developers are allowed to build as much as they want vs the bay area where supply is extremely restricted.
I thought what the OP was suggesting was if people are not buying houses then they are renting them, which may put pressure on the supply of rental properties which are not the same set of homes. In the short term a given house does not instantly transition from for-sale to for-rent.