No reason justifies disbelief.

[The Grand Nudger]

Starting with raw experience is an affirmation of empiricism.  A person who has a "religious experience" - that says god spoke to them or revealed something to them, or transported them to some place where they saw some thing..is explicitly invoking an empirical basis for their claim.

You are conflating subjective experience with empiricism.  That's a pretty poor affirmation of science as an exclusive methodology for seeking truth.

As previously commented on, you have misconceptions about empiricism.  Empiricism is the notion that all knowledge is derived from sense experience.  Subjective experience falls under that header.  It's pretty much the definition of the header. Every single sensory experience you or I have ever had has been a subjective experience, and it's brutally difficult to establish any subjective experience that is -not- a sensory experience.

"I think therefore I am."
You: You are observing your subjective experiences as objects, so that's an empirical realization.  Congratulations, you're doing science!

It could be an empirical observation, though simply making an empirical observation falls short of doing science.  If you hen take that experience and apply the method, you would be doing science.  

That's fine, if you are willing to accept Buddhist meditation systems and philosophical insight as science.  Sam Harris, I think, might actually agree.

But it's not what we normally mean when we use the word "science," and I don't think that it's what LadyForCamus and others in this thread mean when they used the word in opposition to the idea that insight might be a valid (or valuable) tool for seeking truth.

I wouldn't know, Camus and I are are having a discussion about it, but there's nothing preventing a person from using the method on their intuitions, and intuition may be based on empirical observation, itself. What we have been able to agree on, at least I think...is that even if intuition were distinct from empirical observation and capable of being a basis for knowledge...that just like empirical observation...it is in itself suspect on well established grounds and requiring some method of winnowing down false hits.

Case in point, we have done scientific research on buddhist (and broadly) meditations claims, as well as a whole range of alleged insights and intuitions. Their consistent dual failure to produce results or establish themselves as other than empirical is why both sets of claims have been abandoned by all but the most credulous researchers. Don't get me wrong, more power to the folks who keep beating their heads against that wall. They could always discover something tomorrow, just like the sun may not rise tomorrow.