Amos, you're right, the rule is definitely that "if it IS data, it damn well WILL fit the model" - in the same way that Newton and Einstein reinvented the models of the solar system to fit data. As the joke goes, "Scientists make the worst managers; give them facts and the buggers change their minds." ;-)
You mentioned experiential evidence, using people's experiences as evidence. While people are going through these causes and effects fairly systematically, it's almost inevitable that sooner or later, something that previously was explained as "just because" will find a physical explanation. (Whether this is a "just because" from the medical side where they didn't know or claimed to know but were wrong, or a "just because" from the religious/spiritual side who claim it's a spiritual manifestation or a message from God, it's immaterial.) It's happened in every other area so far, which is why some religious folk get riled up about the "God of the Gaps". So it'd be pretty unlikely for this not to happen when people investigate brain functions. In this case for example, they've found one way of causing a brain malfunction which simulates an out-of-body experience. For another example, there's also interesting things they can do with electromagnets which makes it feel like being on a roller coaster without ever moving (strictly that's affecting the inner ear, but it's affecting perception of reality).
In other words, we're putting people in barrels, throwing them down that river, and tracking their reported experience against the initial conditions. We might not be able to see all of their progress (perhaps the river vanishes down a cave) but we can use their reported experiences and what little we can see to try and figure it out. And if we drop a load of people in at the same point at the same speed, and they all report the same experiences at the end, we can be fairly sure we've got it nailed.
Sure, this doesn't mean it's the *only* way that things could happen - in the same way as the existence of gravity doesn't discount the existence of a god personally moving planets around or of telekinesis. But at this point Occam's Razor *does* kick in - we have a known mechanism already, so do we need a further explanation which can never be tested? If this mechanism doesn't work for all cases then clearly there *is* a further explanation needed, but if you want to suggest a further explanation then the first requirement is to show where the proposed mechanism breaks down.
Of course, anyone experiencing this will say "but it didn't feel like my brain malfunctioned". Which asks the question of what *does* a malfunctioning brain feel like, and also hits the problem of whether people will admit to this being a possible cause. Which I know is a bit of a catch-22, but the problem with your qualitative experiences is that there's only one observer, and that observer is anything but dispassionate about the results.