Researchers at Stanford University have discovered that the brains of patients with ME display abnormalities in the white matter within the right hemisphere. It is crucial to further the research involved with these findings as they may lead to more definitive diagnoses of ME.
They repeat an idea that got advocated in the past, and you see MDs still believing it (and thus it gets repeated in the media, and the general population believes it). However, language research using fMRI and other methods has largely debunked that general idea. It's very incorrect to say 'Right-handed people almost always have language organized in this fashion exclusively in the left side of the brain'; there's a large body of research indicating this. 'Language' isn't one thing. It is based in many different components that are complex in their own right: semantics, syntax, pragmatics, memory, and so on. All of those have been shown to rely on both hemispheres.
Nonetheless, from a research perspective, it makes sense to worry about handedness/footedness, as there may be some differences in neural organization - but this doesn't mean that language is 'organized' in one hemisphere or the other. It's far more subtle and complex than that. Since individuals who rely on their right hand/foot predominate in society, it makes sense to restrict research to include only them to reduce some cross-participant variability (and well-done research generally also is worried about the strength of the preference for 'right', and perhaps even first degree relatives' preference). Obviously, this approach tells us less about left handed/footed individuals, but since they are fewer in number, it is difficult to get enough of them as participants, and there seems to be more variability amongst the 'lefts' compared to the 'rights'. So, research tackles the easier case first, with the hope that understanding gained there will help everyone, or at least drive research further.