@MeSci - It could, perhaps - but it's really, really speculative at this point whether or not that might be true.
We know based on a number of studies that C4a is elevated after exercise in healthy people, and there are also studies showing elevated C4a in Lyme and ME patients, sometimes dramatically elevated. If we have autoantibodies that fix complement (IgG, IgM), then potentially, it could be a combination of those factors.
The question would be why, if we have some autoimmune disease, are we affected by just an unusual kind of post exertional malaise. I tried early on in my illness to explain this to so many docs, and they just couldn't get their heads around it. They all understood fatigue from cardiac failure, or liver failure. The latter is virtually always present, and the former is present on exertion - at the moment of exertion. However, doctors knew of nothing that caused delayed post exertional malaise. It simply made no sense to them and fit no disease they knew, so they dismissed it as unimportant.
It's possible that unique among autoimmune patients, the epitope recognized by an autoantibody is variably present depending on exercise because it is not a natural part of our bodies, but a modified antigen produced somehow through exercise. These could fit with Dr. Edwards idea of a less normal autoantibody (I forget the phrase he used).
The elevations in C4a would suggest to me that the classical (antibody mediated) complement pathway is active, as C4 is part of the C3 convertase in the classical and MBL pathways, but not the alternative pathway.
I think we'd have to ask questions about how much membrane lipids actually become oxidized during exercise. Is it enough that it could matter? Is there a localization of membrane lipid oxidation? If they did become significantly oxidized, and this generated an epitope that could be recognized by an autoantibody, then that could trigger the complement cascade. In this case, you'd expect CH50 (broad measure of classical complement activity) to be up. The MAC (membrane attack complex) would form, and the cell would be damaged or destroyed - this is a problem perhaps, as we don't see much evidence of any end organ damage in ME. Patients do not suffer liver or kidney failure, for example. However, there have been reports of increased apoptosis, and Dr. Hokama's work showed increased circulating cardiolipin. This is interesting because cardiolipin (found in the membranes of mitochondria, and hence, in the heart) could be evidence of cell death. Then there's the question of which cells are dying? Is there any preference for one tissue type or another? It's just really hard to know.
We don't really have the information to answer any of these questions, but it's an interesting, if very speculative, theory.