Renting is often more expensive in monthly recurring costs for various reasons. The really big one is that the landlord probably has a mortgage and wants to make a profit. This ignores some properties being under rent controls and government-assisted rent.

A mortgage does generally require a down payment, but if you're willing to pay private mortgage insurance (PMI) monthly you can get as low as 3% down payments in a conventional mortgage and sometimes no down payment in government lending programs. Interest rates vary over time. In the late 1970s even a well-qualified couple was paying double digits in APR. My most recent refi is around 3% over 20 years. Bigger loans can go lower. Shorter loans can (but don't necessarily) go lower. When your balance is small enough, lenders will sometimes charge more interest on shorter terms to dissuade you from taking those. Buying a new home is usually at a bit lower interest than refinancing an existing loan, but market conditions vary enough that's not always the case either.

Then there are taxes, tax exemptions, insurances of varying types, and home maintenance. I didn't dig deeply into the article's methods or data, but if they are comparing rent to only a mortgage they're doing it wrong. Owning property in the US means city and/or county property taxes, school district taxes, sometimes special district taxes (water supply/levee/fire protection/park districts as just some examples), maintaining the property, insuring the property against fire, wind, sometimes earthquake, sometimes mine subsidence or other sinkhole issues, sometimes floods (which by law go through a single government agency), medical for people hurt on the property, contents of the home, and general liability. When renting a property out, often the landlord insures their interests in the property but covers no contents. The renter then assumes responsibility to insure their own contents of the proper and often are required (but it's always a good idea) to insure the property against damage they might cause. Waterbeds often involve an extra policy rider, as might other things.

Of course prices differ based on structure type and location. Unless they controlled for some neighborhoods being majority owner occupied and others being mostly rental property, there's another blind spot in their analysis. Especially in areas with very dense inner cities and lots of single-family homes on private lots in the out rim of the city or in the suburbs, there are some really complicated comparisons. If you're in a 20-story apartment building in Manhattan the land is worth a lot, but you're vertically stacked and probably have decent maintenance crews shared across the whole building. If you've got a 4 BR 3 bath house of your own on a 10,000 square foot lot outside of Houston, the taxes are lower per square foot and so is the cost of the land, but you're responsible for the whole thing. The Manhattanite probably uses mass transit a lot and may not even own a car. If you're outside of Houston, your household has at least one car or your lifestyle gets very expensive in time and/or money very quickly. Your home insurance also suddenly has to cover hurricanes, and car insurance rates are some of the highest in the country.

It's difficult with much certainty to do an apples to apples cost comparison across one whole metro compared to another whole one if you're looking to keep lifestyles the same. The typical Manhattan household is not the typical Atlanta one, but maybe parts of Queens are a lot like parts of Chicago.

Means are means and medians are medians. Those can be useful and make interesting comparisons on the large scale. If you were actually looking to move or to make a rent vs buy decision of your own, then your housing style, home size, commute, tax rates, insurance rates, and mortgage offers are what will matter to you. Even within one metro area people make a tradeoff between a shorter commute and a bigger house or between lower school taxes and better public schools.