Here's what the Bureau of Labor Statistics' FAQ has to say on CPI and housing costs:
Q: The CPI used to include the value of a house in calculating inflation and now they use an estimate of what each house would rent for -- doesn't this switch simply lower the official inflation rate?
A: No. Until 1983, the CPI measure of homeowner cost was based largely on house prices. The long-recognized flaw of that approach was that owner-occupied housing combines both consumption and investment elements, and the CPI is designed to exclude investment items. The approach now used in the CPI, called rental equivalence, measures the value of shelter to owner-occupants as the amount they forgo by not renting out their homes.
The rental equivalence approach is grounded in economic theory, receives broad support from academic economists and each of the prominent panels, and agencies that have reviewed the CPI, and is the most commonly used method by countries in the Organization for Economic Cooperation and Development (OECD). Critics often assume that the BLS adopted rental equivalence in order to lower the measured rate of inflation. It is certainly true that an index based on home prices would be more volatile, and might move differently from other CPI indexes over any given time period. However, when it was first introduced, rental equivalence actually increased the rate of change of the CPI shelter index, and in the long run there is no evidence that the CPI method yields lower inflation rates than some other alternatives. For example, according to the National Association of Realtors, between 1983 and 2007 the monthly principal and interest payment required to purchase a median-priced existing home in the United States rose by 79 percent, much less than the rental equivalence increase of 140 percent over that same period.
Ordinarily, because people can substitute between renting or owning a house, the price of a house should broadly reflect its rental value (e.g. if it were much cheaper to rent than to buy then people would stop buying and start renting until prices 'equalised'). However, if a bubble is being driven by speculation on future house price increases then it is likely that house prices will become decoupled from the long-run rental value of a house. You can see what this looked like during the last housing bubble in the below figure. It can clearly be seen that house prices (the blue line) were not well-reflected by the owner-equivalent rent included in CPI.