Does the SEC regulate the CDS market?

Lars Toomre (via Alexander Campbell) thinks that yesterday’s SEC actions are just the first shoe dropping:

Toomre Capital Markets strongly suspects that more forthcoming enforcement actions will be filed in connection with the use of credit-default swaps and the use of inside information. The SEC’s unprecedented sweep of Wall Street’s equity trading records for the last two weeks of third quarter of 2006 coupled with information requests about prime brokerage funding activities during that period strongly suggests that certain leverage players (i.e. hedge funds) are going to have to explain why they were trading in certain securities just ahead of market moving corporate actions. TCM has no idea whom exactly is involved. However, CDS spreads have been moving too much ahead of unusual corporate events.

The issue of CDS spreads moving ahead of private-equity deals is known, and is a big one. To quote myself:

LBOs, by their very nature, need a lot of debt. That debt comes from banks and, increasingly, from hedge funds. And when those banks and hedge funds provide debt financing for an LBO, they hedge their positions in the CDS market, driving prices up.

But I am far from sure whether this kind of thing is likely to get prosecuted by the SEC. For one thing, it won’t show up in a “sweep of Wall Street’s equity trading records,” since equities aren’t involved in these trades. But much more to the point, hedge funds aren’t “going to have to explain why they were trading in certain securities just ahead of market moving corporate actions,” because CDSs aren’t securities.

So I’d love to ask the question, if anybody can help: Let’s say, for the sake of argument, that there was a cut-and-dried case of a hedge fund loaning money into a private-equity deal, and hedging that exposure in the CDS market before the deal was made public. First, does such activity fall within the purview of the SEC, and second, in any case, is it actually illegal?