This is why most angels have to be accredited investors, meaning that they need to have $1MM in assets. Millionaires investing in new ideas aren't exactly naive widows and orphans (though they could be). With public stocks there is indeed high liquidity, but there was also strikingly high volatility during the tech bubble. It's good to be able to sell your shares, but less so if the price can drop 80% in a day. That'…
Well he explicitly mentions equity crowd funding which allows people to bypass those rules. Also, from personal experience as an angel investor, there isn't really a great authority out there enforcing accredited investor requirements. All the times I've invested in private companies, I simply had to sign a one-page document self-proclaiming myself as an accredited investor.
As for the more fast and loose, "crowdfundy" sites? I have no personal experience there, so no idea. I don't see the upside in investing through them.