Why would that be the case? This is an issue of allocation, you can't read that off of aggregate supply and demand curves.
If there aren't enough houses for people to live in as the market could bear, that's an issue of building more houses, not who owns the current houses.
It's not just about the number of homes. It's also about the prices of those homes. The crisis is not necessarily that people literally can't find a place to rent; it's that they can't afford it.
Maybe the analysis in the underlying report is flawed (and it very likely could be), but that's the claim. It's not a claim about what might happen, it's a claim about what is happening.