It's funny that you even think that's what's happening when people stop eating gluten. As evidenced by this study, the literature supports neither the conclusion that gluten causes these symptoms, nor that it does not.

I am not making a generalization about everyone who experiences these symptoms. I am speaking form my personal experience in dealing with people who demonstrably do not have a gluten intolerance, despite their claims to the contrary. I know this is the case because, oddly enough, they only ever experience a "reaction" when they are aware that they're eating gluten. I have personally seen, on multiple occasions, people who make this claim unknowingly consuming gluten with no ill effects. These are the people I'm talking about, and I feel like I made that very clear (at least, to anyone who isn't actively looking to be offended). I have no doubt that many people who claim gluten sensitivity are indeed experiencing real symptoms; what I'm saying is that, at this point, the science does not support blaming it on gluten. I'm also not writing off the idea that gluten is indeed responsible, but rather saying that coming to that conclusion is premature.

The anecdotal evidence we're left with is that some people feel better when they make dietary changes associated with avoiding gluten. The only scientifically questionable part of this is "what dietary change produced the change in symptoms?"

Wrong. This is completely begging the question. Before we ask "what dietary change produced the change in symptoms?", there are a whole host of other questions we must answer. Was there actually a measurable reduction in symptoms, or is this a case of self-reported confirmation bias? Is there actually a physiological response here, or is this a case of the nocebo effect? Are the reported symptoms explicable by any other possible factors besides diet? Are there other possible explanations for the reduction of symptoms? These are just a few of the many possible variables that need to be considered before concluding that a change in diet is in fact responsible for the reduction of the symptoms in question.

You seem to be questioning whether these people even experience the symptoms they claim to experience, which is not scientific questioning but solipsistic metaphysical arrogance.

Again, that's not what I'm doing at all. That's just what you're taking from it because you're clearly looking for a fight, not a conversation.