People would be able to direct their SS contributions to a fund that is invested based on several thing. Age, risk tolerance, etc. You would be able to choose growth mutual funds, fixed income funds, international funds, REIT funds, in whatever combination you were comfortable with.
It would operate much like an age-based 529(b)plan where younger investors would have their money go more heavily into growth funds, and as you got closer to retirement age that money would gradually move to fixed funds to reduce the volatility.
It sounds like a great plan to me. No individual stocks. Managed by mutual fund type managers where each account would be vastly diversified. Even if you choose 100% growth funds, you would likely own a small piece of 200 - 250 different companies within a single growth fund.
It's nice to see that they're actually doing a public survey. While I'm shocked that NPR actually reported it!