Best calculator I've found (http://www.nytimes.com/interactive/2014/upshot/buy-rent-calc...), given standard values like a 4% mortgage with a 20% downpayment and a 5% investment return rate, shows your scenario break even at best over 30 years -- hardly "large and unambigouous margins".
That's an okay one, it's broken in some ways (assumes you're selling your home after the mortgage is up, or that buying 100% of the home up-front doesn't make any long-term differences. It doesn't figure into standard of living deltas over time or time-value of money.)
So now it's just your reasoning that's broken.
Here's the tl;dr - You need to pay for housing no matter what. Do you buy and rent out your property to somebody who'll pay your mortgage and costs for you? Or do you pay those costs for somebody else? Assuming an equal start, the property owner comes out somewhere around $1-2mil ahead of the renter over 30 years, and has housing in the end.
For those parameters, on a $500k property, you would need to find an equivalent property to rent for $1,491/mo for 30 years for renting to be "better". After which the renter has no housing and the owner has housing into perpetuity.
Good luck finding equivalent housing under $1,491/mo for that kind of property. In most areas in the U.S. at least, an equivalent property rents out for far higher than $1.5k/mo. In the areas I spot checked it was more in the range of $2.5-$3k/mo.
This assumes the owner only ever keeps this particular mortgage, never pays down the principal, never rents any of their rooms out or takes any other cost saving measures that aren't available to the renter.
Meanwhile percentage of income required to live in that property will stay the same for the renter while going down (relatively) for the owner.
If you fiddle with the down payment slider, you'll note that no matter what it's set to, it doesn't make all that much difference in the ratio. Set it to zero since you can finance 100% without too much fuss. Now this sets things as equal, there's no additional money to invest for the renter other than some imaginary delta they would save by renting at rates far below any available realistic market rental rate.
The renter still has to find property to rent about a thousand dollars less than the going rental rate in the market he's in, then still has to find housing at the end of the 30 year period.
If the owner decides to sell at some point along the way, they can convey the stored value of their property into their new property. The renter has simply burned all that money and will rent forever, at increasing nominal costs pegged to inflation or current market forces (whichever is greater).
So that I don't have to repeat myself again, here's an excellent write-up on the topic. Assuming an equal start, the property owner comes out somewhere around $1-2mil a head of the renter over 30 years, and has housing.
"In the areas I spot checked it was more in the range of $2.5-$3k/mo."
Exactly my point. The rent has to be above the mortgage payment by a good deal to make buying pencil out. If, as in your example, the equivalent rent is 25% less than the mortgage payment would be, buying doesn't come out ahead at all, nevermind by "large and unambiguous margins."
Your analysis link makes the same handwavey errors you did in your initial breakdown -- maintenance costs far too low, ignoring other costs involved with homeownership, etc. Interestingly enough, the link has a postscript where he redoes the analysis after people point out those errors with just a couple of those factored in (not all of them) and concludes that the renter would just about make his money back -- and that's with a rent payment about the same as the mortgage payment, not 25% less.
Best calculator I've found (http://www.nytimes.com/interactive/2014/upshot/buy-rent-calc...), given standard values like a 4% mortgage with a 20% downpayment and a 5% investment return rate, shows your scenario break even at best over 30 years -- hardly "large and unambigouous margins".