One thing that we know is that Lyme bacteria makes a toxin very similar (but not identical) to toxin made by some species of mold. (Dr. Ritchie Shoemaker discusses this in depth in some of his books, such as "Desperation Medicine.")
If that is the case, and if CFS is driven in part by the presence of mold toxin, then it would make sense that Chronic Lyme and CFS would present with similar symptoms but be distinguishable by protein analysis.
However, even if this is the case, in many/most/all cases it's still likely more complex than a case of mistaken identity. For instance, Shoemaker reports (and I agree, based on my observations) that having a history of toxic mold exposure can (for genetically susceptible people) make Lyme disease more severe and more difficult to treat. And having a history of Lyme disease can make subsequent exposures to toxic mold more damaging, he suggests. Apparently the toxins accumulate in the system over the long term and contribute to the illness in additive (or maybe even multiplicative) ways.
We have enough case studies now to suggest that many/most/all people with CFS react strongly to very small amounts of mold toxin (e.g. contamination of objects stored in certain moldy buildings). Many people who define themselves as Lyme sufferers (including those who got sick following a tick bite) also respond to very small amounts of toxic mold.
My own suspicion is that the reason that many people benefit from antibiotics to treat Lyme even though they do not show up as having any unusual amount of Lyme bacteria on Lyme tests is that they are reacting to tiny amounts of Lyme toxin, and thus need to get rid of every last spirochete and cyst in order to get the toxin levels down to a level low enough that they're not bothered. It would be nice to see studies on this.
Dr. Klinghardt, who is one of the most prominent Lyme doctors, recently stated that the most effective way to treat Lyme patients is by looking at their living conditions and having them move if they're getting big mold exposures. And though not everyone in the Lyme community feels that they have the ability to move from bad places, the importance of considering mold is now a regular discussion topic on Lyme boards.
So I'm going to suggest that it would be a mistake to take away too much from the studies listed above with regard to the idea that a lot of Lyme patients are "misdiagnosed" as having CFS. Rather, I think that Chronic Lyme and CFS are overlapping illnesses, and that both Lyme and mold (including internal fungal infections) need to be considered in all patients regardless of what label they choose to use.
Of course, if people are going to define CFS as "mystery disease" (to be treated just with palliative drugs such as Florinef), then I can see why rediagnosing that illness as "Lyme disease" would be a step up (even when, as is the case here, treating the Lyme component results only in improvement rather than anything approaching wellness). I think we can do better than "mystery disease" at this point though.