I don't think that's true. The private renters also have to abide to the regulated market prices, so you cannot buy your way to a rental apartment. Not unless the renter is breaking the law, that is.
I admit that I pulled the 20 years stats out of a hat. I quickly looked for some stats, and this page suggests around 10 years average for the private market, and 13 years for the communal: https://www.stockholmdirekt.se/nyheter/sa-lange-maste-du-koa...