There are two issues in your reasoning.
First, you're assuming that they own the place outright. That wasn't the case for the immigrant in the top level comment.
Second, you're making the bizarre implicit assumption that the market for buying housing and renting it are fully independent, which couldn't be further from the truth. Increasing real estate prices contributes to an increase in demand for rent, as less people can afford to buy housing and must rent, until there are no more would-be homeowners that can't afford a house and must rent.
Those units are getting sold, one way or another. They're either getting sold to a landlord or a homeowner, so until there aren't enough units for rent for people that don't want to buy, and we are very far from that, it being sold a landlord means one less homeowner.
By the way, this is a huge issue in New York City - landlords that have a mortgage, like the one the OP had mentioned, can't afford to lower rents because that would break their mortgage agreements and force them to renegotiate it which they can't afford, so they would rather keep vacancies than rent at lower market rates.
Otherwise, if someone adds actual housing supply then it can be worth increased systemic risk. If they aren't, there is no upside to the downside.