That's what you should do when your mortgage would be substantially greater than your rent.
A.L. Williams, the insurance man, didn't say "Rent and Invest the difference," but he could have. What he actually said was "Buy term [life insurance] and invest the difference."
There are two kinds of insurance, term, and whole life. With "whole life," you're insuring against a certain proposition, your death, and basically betting on whether or not you beat the actuarial tables. With term, you're betting that you won't die within the next X years of the term. So term is much cheaper. Investing the difference between the two types of premiums is the best thing you can do for your retirement. It's something that even a former high school basketball coach could figure out (and build a major company, AL Williams Companies, around).
Renting versus buying a house is a tougher analysis. Sometimes (like now) renting is cheaper. At other times (e.g. right after World War II) buying was cheaper. In either case, a wise investor will pick the cheaper option and pursue it.
According to fellow seeking alpha writer Jason Tillberg, one person that didn't make such as a wise choice was none other than Treasury Secretary Tim Geithner, who pays perhaps $10,000 a month on a mortgage for a house that he could rent for $7,500. The difference is at least $2,500 a month or $30,000 a year (not counting additional expenses), which for most people, is a nice chunk of investment capital. .