I disagree. If inflation is very high, the fed (aka BOC for me) will increase the interest rate, and by correlation, a higher mortgage rate ensues. Less people qualifying for mortgages attacks the demand side of the market, lowering the prices of homes.
While they make up the moajority of new home loans, they only make up ~15% ot total mortgage originations, leaving 85% of homes being mortgaged with conventional mortgages.