I'm willing to bet that excerpt refers to mortgages that are exempt from the requirement of having mortgage insurance, rather than all mortgages, for everyone.
The way it currently works with most private lenders (i.e. not FHA or the like...) is, if you cannot put 20% down, you are required to pay mortgage insurance. Many people who cannot put 20% down either 1. go through one of the government-sponsored programs or else 2. they pay mortgage insurance on top of their montly payment, and when they reach 20% equity, that mortgage insurance gets removed.
In other words, a person can put $5,000 down on a $95,000 mortgage, to buy a home valued at $100,000. That person only has 5% equity in the house, (not the 20% that is considered really "safe" and which used to be standard back in the day, prior to the boom. Probably your grandparents or parents saved up and put 20% down, if they even had a mortgage at all, because decades ago that was standard operating procedure. That's what you call skin in the game -- they buyer assumes some of the risk, and is not motivated to default on the loan. Banks actually don't want houses, they prefer people to be able to easily pay back their loans.)
But with 5% (or less) down, the bank assumes more risk, and the buyer has less incentive to not default. So, to mitigate that risk, and to make homes more affordable, they have mortgage insurance. On top of your monthly payment you'd pay, say, $30 a month for mortgage insurance which protects the lender in the event you default on your loan, since basically, you are stretching to afford that loan. Once your loan balance is down to $80,000, the mortgage insurance goes away, cause you've assumed more of the risk.
And with FHA loans and the like, the government assumes more of the risk. And more people can afford homes, and demand goes up, and that drives prices up... and we all know what happens then, right?
so anyway, that's probably what the 20% thing is referring to, I bet.