The New York Times published the same sort of analysis in 2011:
http://archive.nytimes.com/www.nytimes.com/interactive/2011/...Be sure to carefully read the description of the graph. Every time I link this, someone assumes that the green & red indicates are the yearly returns, but the entire point of this graph is that it is cumulative. If it is red 20-30 years into the line, that means that money put it at the beginning had a negative cumulative return after 20-30 years, not that the 20th or 30th year was negative. Also observe the graph is inflation adjusted.
Yes, it's true. The idea that you can just stick your money in the stock market and see 7% returns every year is somewhere between "mistaken" and "a lie". It is not a coincidence that this idea has arisen during a time of loose monetary policy and a stock market that is being inflated by it over the course of a couple of decades. In the 1970s and 1980s, for instance, this would have been considered risible, and indeed, people did not generally value stock equities. (See the chart for why they may have felt that way.)
It is not an even remotely accurate model of the stock market to think of it as a 7% return that you can casually compound over time. Anyone who speaks of that model or uses that model doesn't know what they are doing. Your debt certainly compounds over time, but your assets can't be modeled as doing that.
A couple of further observations:
Part of the reason why the stock market can offer 7-10% gains in a year, when the economy does not offer such gains in general, is precisely that "room" is made for those gains by the years in which it loses big.
This is also part of why we have a pension fund crises, because even in the relatively friendly stock market of the past couple of decades, even these so-called professionals would blindly use a high-single-digit return estimate per year, and even in the past few years, that has been an inadequate model. The bailout they're going to need if the stock market actually crashes (popping the "Everything Bubble"?) will be literally unaffordable. (Not paying in sufficiently is also a problem, but that is also itself a consequence of absurdly optimistic models being generally accepted.)