You're forgetting that the price of any new owner-occupied property must also price-in the opportunity cost of not renting out that property. Nobody buys a house when they could get rich by renting out the same house to someone else. Indeed a foreign investor is likely to buy it, because it's a great source of income, and they already have somewhere to live.

If I can rent a property out for thousands of dollars a month, that property is worth a lot of money. So it's really the rental market that is pushing up prices in the owner-occupied market.