Were they to find similar biological abnormalities in FMD and ME/CFS, it would not prove that they were both functional. It would prove the opposite, i.e., that they are both biological illnesses. Functional illnesses do not reveal biological abnormalities.
It's only if they find nothing abnormal in both diseases that they could say that the lack of findings suggests that both diseases are functional.
They don't need FMD for this purpose, since, I assume, they also have a control group.
I can only speculate that they have some amount of money budgeted for FMD and they are including FMD to increase the overall budget for the ME/CFS study. This seems like something you would do if you were told to go "find" money for an ME/CFS study when none had been budgeted.