The article also forgets a lot of second order effects that affect much of Spanish home ownership.
For instance, Franco's rental laws have been weakened, but not by that much. Even when you could theoretically get evicted, a savvy lawyer can easily extend a renter's stay at an apartment, without really paying a dime, for about a year without facing eviction.
There's also pretty weak protections for renters whenever an apartment is vandalized by its occupants. It is not uncommon to hear stories about tens of thousands of euros of damage deal to apartments as retaliation to an eviction.
There's also rent controls that make San Francisco seem like a libertarian's wet dream. The longer you hold an apartment, the less likely than you'll want to leave, and the less profitable it is to the owner.
Such legal frameworks make apartment buildings that are built and designed for renters, managed by a company, to be an exception rather than the rule. There's just too much risk to take something like this on. So most rentals are really by people that own 4, 5 apartments, and select the renter's very, very carefully. For instance, my sister got a rather good deal a few years ago on a little apartment for her and her husband, she was pregnant at the time. The reason the price was so good was precisely that she offered an extremely low risk for the owner: The apartment will get too small for my sister's family by the time the kids stop being toddlers, she has great family references, and her job requires her to have a good public reputation. So she is a very small risk of staying there for very long, of damaging the apartment, and of becoming delinquent. A recent college graduate born in a different state and with a job would not be able to get the same deal, because of the different risk profile.
Another part that it's not mentioned in the article is when your average Spaniard stops living with his parents. Unlike in the US, when adolescents move out of the house to go to college, many Spaniards will live with their parents until they get married, and Spaniards don't marry young. This makes the share of owned houses pretty high indeed, as living with mom does not count as renting.
Spain's cities are extremely comfortable to live in, if you happen to have a job, so I do not expect the number of elevators to change. Number of renters, on the other hand, could be changed pretty quickly by legislation: Protecting renters actually makes renting harder!