If a house is being rented it means I can't buy it, supply is low. That's what I understood housing supply meant when talking about house prices. Renting is not a factor, it's another market.

Renting is not an entirely separate market... renting is an alternative to buying, and their markets are linked.

"Housing" is the market, and renting and buying are two options for people in the market.

Even assuming the markets were separate, if corporations were buying up tons of housing stock and flooding the rental market with it... shouldn't rents be going down?