Abaddon,
That's the problem with believers. They get so wrapped up in the subjectivity of belief, in their personal experience, in the elevation of personal opinon to an object of worship, they fail to consider that other people with beliefs (unprovable just like their) have contradictory experiences, beliefs and opinions.
I have a few questions for you regarding this snippet of your post.
(1) Is it possible to have an actual personal experience and conceive a framework through which to interpret that experience while being unable to prove the experience and/or framework through verbal medium?
(2) Is it possible to have an actual personal experience that is not verifiable by testing and which may not be shared by all people?
If both or either of these is true, then...
(3) Is it possible to have personal facts, that cannot be proven to anyone else?
The reason I ask is because I know the answers to #1 and #2 are "yes", and therefore the answer to #3 is "yes", but I also acknowledge that you may not know that. If you don't know #1 and #2 are possible, there is no way for me to prove the possibility to you except through thought exercises. Which I can do.
Respectfully,
AuldSoul