I'm wondering why they chose 15 / 20 as the cutoff ratios though. I'm a licensed real estate agent in NYC and I've helped a number of clients make purchases where it was actually cheaper to buy than rent (usually a studio or 1BR, or outside Manhattan).
It seems like you can finance a home purchase these days at 5% or less on 30-year fixed. Add in the mortgage interest tax deduction and you are really borrowing at 3.00% (assuming your marginal tax is 40% including state / local taxes, which would be true of anyone buying a $1.3M 2br as referenced in the site).
That seems to justify a break-even ratio of about 33, not 16 or 20. Of course, you do have to add back HOA dues / coop maintenance + property taxes, and the nasty transaction costs for buying and selling. That is somewhat tempered by your rent (and property values) going up with inflation while your mortgage payments are fixed. Therefore, all the usual disclaimers apply that you need to be willing to stay there and own the property for quite some time.
EDIT: clarified that 5% rates are for 30 year fixed mortgages; 15-year amortizations would get 4.25% or so, changing by the day.
EDIT2: The tax deduction is LESS good in other metro areas. When I used to live in Redmond, WA, my marginal rate was not 40% (there is no state income tax in WA and houses are much cheaper). Also far more subtle but often ignored, in Washington most renters would take a standard deduction and only home-owners would itemize their deductions. Itemizing mortgage interest means you lose out on the standard deduction. In NYC, just about everyone itemizes because state / local income tax is already compelling enough to do so, therefore almost all the mortgage interest is deductible except for the amount subject to Pease provisions.