The article's analysis missed one big thing in the comparison: rent (necessarily) includes a profit margin for the owners. In a mortgage this is the interest payment on the loan, but in a mortgage the owner gradually shifts from lender to buyer. (In fact, one way of looking at paying down a mortgage early is that the buyer is earning higher returns at the expense of the lender.)

It wouldn't surprise me at all that a mortgage, after accounting for all factors, is still cheaper than renting.