The house that sells for $200,000 might rent for a range of monthly numbers. 3% would be $6000/yr or $500/mo. This is absurdly low, and favors renting, not buying. 9% is $1500/mo in which case buying the house to live in or rent out (as a landlord) is the better choice. At this level "paying rent" should be avoided.
I'm simply explaining the author's view, not advocating it.
A quote from the article -
annual rent / purchase price = 3% means do not buy, prices are too
annual rent / purchase price = 6% means borderline
annual rent / purchase price = 9% means ok to buy, prices are
Edit to respond to Chuck's comment -
Mortgage rates for qualified applicants are pretty tight from low to high, the 30 year is about 4.4% and the 15, 3.45%. Of course, a number of factors might mean paying more, but this is the average rate. And it changes over time. But the rent and purchase price in a given area will be different. Very different based on location. See what you'd pay for 2000 sq feet in Manhattan vs a nice town in the Mid-West.
One can imagine a 'heat' map, when an area might show an $800 rent on a house selling for $40,000 as a "4.16" (The home price divided by annual rent) and another area as a "20", where the $200K house might rent for $1667/mo. It's not homogeneous through the US. As I said, I'm not taking a position, just discussing how the author formulated his approach.
The author makes some assertions that can be debatable, e.g. that low rates are a bad time to buy because they already pushed the price too high. In my opinion, the US has had the crash, but the rates are still low. Buying is a personal decision, and the own/rent ratios are only one tool to be added to a list of factors in making the decision.
Of course the article, as written, does the math based on the rates at time of publication (4%/30years). And the ratio of income to mortgage one can afford is tied to the current rate. The $60K couple, at 4%, can afford just over a $260K mortgage, but at 6%, $208K, and 8%, $170K. The struggle isn't with the payment, but the downpayment.
The analysis isn't too different for a purchase to invest. If the rent exceeds 1% of the home price, an investor should be able to turn a profit after expenses.