Although EB-5 is an immigration program, all laws and regulations of the United States apply to its participants. The "Accredited Investor" requirement is due to the federal securities laws. When you make your investment into an EB-5 entity, you are buying securities of that entity. As a result, U.S. securities laws apply.
In order to be exempt from the registration requirements mandated by the securities laws, it is necessary to qualify for a valid exemption. Most EB-5 deals are done in compliance with the Regulation D "private placement exemption" and/or the Regulation S "offshore offering exemption." Regulation D provides that all investors in an offering must be accredited investors.
The accredited investor requirement of Regional Center is not an immigration requirement, it is an SEC’s requirement.