True enough but for purposes of argument a 50% decline in housing costs does represent a 50% increase in the value of the dollar visa vie housing no?
When you say relative the housing, your statement becomes technically correct. Most people simply don't speak of the value of the dollar in this context. They refer to it with respect to foreign currencies because those affect the entire economy or with respect to a representative bundle of goods for precisely the same reason. Any one good is so unrepresentative of the ecocomy that most people would prefer to say that it is that good that changed its value --- relative to a representative bundle of goods, hence with respect to the dollar.