The articles scenario assumes that the supply is elastic (and only bound by rent controls), while the demand is static, which is not even remotely plausible (e.g. see http://en.wikipedia.org/wiki/Urbanization - almost everyone wants to live in a city)

What would really happen is a massive influx of demand, because many people rich people (rich in this context: "Have the means to buy high-priced properties") who do not want an apartment today (because there are none which meet their 'standards', partly thanks to rent controls), would start to move in. This would lead to a situation where a) all new supply would be concretated in high-priced estate, which would still be bought up by the increased demand, while b) the bottom (i.e. todays rent controlled apartments, going with the assumption these are not well maintained and therefore 'cheap') would just go up in price, because there still wouldn't be any new options for the inhabitants of those properties. Result: Higher prices for the current occupants of apartments, a new crop of high-priced apartments bought up by rich people, no better supply of "main street" living room.