I don’t think the relationship between rates going up and prices going down is so cut and dried. Look back at the early 80s – mortgage rates went well into the teens and home prices did not drop. Market activity shrieked to a halt, or so I’m told, but prices did not actually go down.
Generally speaking, there has been very little historical correlation between rates and housing expensiveness.
That said, a sufficiently violent rise in rates could certainly take down housing prices (especially given all the other factors in play). But I just don’t think it’s the done deal that a lot of people think (ie, “It’s ok if rates rise because prices will go down”).