I think the SEC is a civilian regulatory authority. It’s not the same as a criminal investigative service like the FBI.
I suppose if someone wanted to investigate the Clinton Foundation, you’d likely use the IRS first maybe?
The IRS is the first place I’d look. If it was found that they weren’t really a charity, they’d be in the hole for a lot of back taxes. After all, it was the IRS that got Al Capone, and its the IRS that decides on whether or not an applicant is tax-exempt (remember Lois Lerner).
But there are likely many other ways in which the rules were skirted or fraudulent, that aren’t just related to tax-exemption.