That is what is implied by the policies we have in place today. I don't believe your intelligence is measured by your bank account, that is the whole point of the comment.
The regulations are not really in place to protect "the poor from their own stupidity." The regulations are in place because the lesson of the Depression is that one person losing their shirt is personal responsibility, and that's fine, but millions of people losing their shirts at the same time will pull the rug out from under the wider economy and be a societal disaster.
The criteria for accredited investors is a very crude way to address this problem by reducing blast radius; we could come up with something more convoluted like requiring a minimum amount of bond posted to act as a floor (similar to how non-insured people driving cars works in some states) but the effect would be roughly the same.
The lesson of the Depression is that the Fed at the time sat on their ass and let the economy collapse around them instead of doing something. It had little to do with retail investor euphoria.
Wasn't that a synopsis of Ben Bernanke's entire output over his whole career? Personally I don't completely agree, especially as Bernanke used that theory to justify some of his own questionable actions...