If you find ibuprofen works in an unselected population of people with joint pain then you can expect it to work in a patient with RA who has joint pain, unless you have a specific reason to doubt it.
I think here the discussion could go on and on...

meaning, in my opinion, your arguments are valid, as the others' are, too.
I think, strictly scientifically, you cannot apply statements/results about joint pain to RA without further steps. Even if it seems logical, obvious or even trivial. We all know that we can be false with our "that's obvious"-feeling. There can be reasons found why you cannot deduce from the one to the other, e.g. the joint pain in RA is not the same joint pain as in joint pain, meaning the joint pain in RA has another origin and/or there are interactions between symptoms/processes leading to another type of joint pain.
I imagine that in terms of sets and ask myself: Is there a subset? If RA were a true subset of joint pain, then it could be logical to deduce: What works for joint pain, works for joint pain in RA. If RA and joint pain are two sets whose intersection is non-empty (but RA is not a subset), then you only can make that statement for the intersection set.
The question is: What are the elements of the intersection? And is there really an intersection? In case of joint pain (let's make it easy) that intersection could consist of one element: joint pain. Or it is empty.
In case of "chronic fatigue" (set 1) and ME (set 2), set 1 and set 2 might also be distinct, i.e. empty intersection; there could be an intersection: fatigue. Or even more: fatigue and headaches. But it doesn't have to. It depends on your selection of cohort. Furthermore, there will always be elements (symptoms) in set 1 that don't lie in set 2 and vice versa.
In my view it is pretty difficult in this case which characteristics of "chronic fatigue" can be transported to "ME", which yould you need to do in order to say "this or that helps".