Nah, rents aren't determined by owners' costs (except at the margin where property owners are debating whether to 'stay in the game') - they're determined by bog standard supply/demand and usually set to the maximum rate the market will bear.
This assumption (which is largely correct) gets thrown out the window when the entire tranche of supply is hit with a cost increase all at the same time (and every participant knows it).
The point of this "margin" you mention gets rather deterministically and uniformily raised across the board.
I don't understand this. The owners have pay mortgage, taxes, insurance, and repairs. How can it be decoupled? The landlords I know would have to sell if they lost their renters, or if the rental income fell below a certain amount.
If the market cost of renting a unit drops below the landlords' cost to maintain the unit, the renter doesn't go "oh well, that's a shame, I guess I will pay the higher amount."
The landlord either eats the loss or gets out of the game. Since vacancy is the worst possible outcome for a landlord, they can't just hold their units off the market to get the price they want.
It's often easier to think about the reverse situation -- imagine there's an error at the bank and the property owner's mortgage goes poof and his cost of operating the rental is cut in half -- do you think he'd lower the rent for his tenants? Of course not.
It's not a perfect market, rents are sticky, landlords don't profit maximize all of the time (e.g. they might keep the rent the same for several years for good tenants), but in general landlords will charge the highest amount they can charge at all times regardless of what their cost basis looks like.