The way the system works, the burden/penalty is on the company, not you, to verify your accreditation status. If you lie on your self-accreditation form, that's the company's problem for selling private securities to unaccredited individuals (and a huge problem it may well be). This is actually one of the big pain points that platforms like AngelList, with their syndicate deals and their self-reporting requirements, solve for startups. AL standardizes the self-accreditation process, and puts up stringent documentation requirements, that make it very hard for a person to lie his way through. Companies get peace of mind that AL investors have the net worth they say they do. FundersClub also does a pretty good job of this, in my experience.
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.